So in summary with the latest information
That would be exceptionally hard to do
That is unlikely to happen in the near future. So the only tyres people are going to get are NR and KG and neither have worked well for people thus far. It does not bode well.
EDIT/Correction: Well actually KG has not been tried but based on what Roger has said I cannot see this is going to be any different from the NR
Presumably the same goes for the Wheel TA.
I still have a TA Tire and it weighs a ton! It would totally negate any weight savings from the carbon rim, and even add some extra.
UDC UK list a light version of the TA alongside the original. I assume that it’s based on the same carcass as the NR Lite, but I don’t know for sure. Out of stock anyway.
EDIT: I just noticed that the SKUs on those tyres are tyre36Quax and tyre36QuaxLight, so maybe they have a different lineage than the original Wheel TA. Hard to say with 36" stuff since a lot of it is (was?) made in the same factory.
After this last explosive blow-off I am totally done with attempting to run pressures any higher than 30psi, with any 36er tire on this cf rim. Not worth the cost of replacing tires, tubes, and the chance of serious injury if it explodes while riding. Not to mention the trauma to the eardrums! Hard pass. At least I can still use it for MUni and hopping up stairs. 
It seems very likely the light TA is produced by Innova in the same factory as the NR and KG. Here is the historical quote about how all the previous iterations of these tyres were made (which predates the Vee T-Monster)
Later Roger talks about the switch over to the new company (Innova).
Anyone with the new “light” TA could likely confirm this by looking on the tyre for a code starting IA-.
P.S. This is also interesting
Perhaps the NR/KG/TA 36" tyres are still slightly “off” and the bead tool needs further correction.
That said, I do agree with the rest of you that correct or not, given the overwhelming majority of 36 tyres are like this, Nextie should have designed their rim in such a way that it works with these tyres. I know they say they have tested a NR but I remain suspicious and even if true they got one a little late in the game and just assumed everything would be fine. You cannot make a rim that does not work with the tyres that people have and are likely to be the only ones purchasable for more than a year.
That’s a very expensive pogo stick! 
Hmm… looking again at the descriptions of the various 36er tyres on UDC UK’s website I do note some differences with regards to max PSI. The light versions of NR/KG/TA are rated for 65/50/32PSI respectively.
Also, the single review of the TA light is by @Piece_Maker who notes that it is “crazily light” (presumably compared to the old one) but also adds,
The TA tyre is a nightmare to mount - don’'t even try it with plastic levers because they’ll snap!
So perhaps (?) tighter on the rims than NR/KG (neither of which I have struggled particularly with in the past)? But even if true, it is still only rated at around the same PSI that @UniGeezer has already settled on. So I am not sure there is much to be gained by owners of the Nextie rims buying this if they already have a NR light or KG light.
EDIT: I had actually always assumed that the max PSI on the KG light was the same as the NR light, given the same underlying construction by the same company, in the same factory. So I just went and double checked what was written on the tyre itself. Sure enough the KG light has “Inflate to max 3.5 bar” written in massive letters down the side (this equates to 51PSI). Now I wonder why these tyres have such different recommendations when they are essentially the same underneath. Particularly the TA light if it too is an Innova tyre as one would expect. 
Nextie are hanging onto their assertions of their rims being technically fine and I’m not impressed. A copy of my latest response to them below:
Looks like the whole problem is that here no specification or standard for the height of the rim edges above the Bead Seat Diameter for a 36" tire/rim. It also seems likely that the Nightrider tire has a inside bead diameter a little larger then ideal. Nextie knew that and should have made a rim to work with the tire at hand. A deeper dip on the middle of the rim (so the tire can be mounted) and higher edges (so the tire can’t blow off) should be doable and work just fine.
I think this is where that comes in.
It seems that they understood that the rim lip may not be high enough, but then at some point along the line decided that it was fine, and we trusted them on that, as they were going to test with a real tyre.
I believe that they had the drawings of the Stealth II tyre, and I don’t know how much communication they had with Roger but I’m sure he could have advised of the problems with the old 36" rims that didn’t like to hold onto tyres as well. As I understand it, that was because the rim lip wasn’t high enough.
Nextie increased the bead retention hump which should help to ensure if it was being run tubeless that the tyre woudn’t slip back into the well, and added and then sharpened up the bead hook to try and keep the tyre on the rim, but clearly that’s not enough.
Especially as they’d already made one rim that didn’t - and we all just wanted a new rim that did.
We never wanted a rim that adhered to a specific technical specification.
I think they just made it to what the specs would have been for other rim sizes and said," f— it!" You’ve got to keep in mind that there would have likely been at least one engineer and multiple industry specialists involved with this. Making bicycle rims is what they do probably 60 hours a week or more and I would guess that as soon as they had both the rim and a Nightrider tire on hand that the problem was obvious to all of them.
Sure but then don’t lie about it 
I wish there was some way they could have just virtually copied the stealth rim and simply made it out of carbon fiber. Problem solved. Unless I’m missing something here.
Not missing a thing, You and a group of like minded riders were used for the expense of research and development for their profit and knowledge.
I’m not sure how much profit has been made but definitely used at our expense for R&D
Well I for one would rather have that technical specification. I don’t ‘need’ to ride my 36" though. I can wait for the consistent tire to match my nice consistent rim.
Without these sorts of technical things… you end up with…I guess…maybe a nightrider situation?
When does the lunacy end? A high end rim to match a low end tire?
Fibs and assumptions were made by manufacturer. We all see that and so do they.
Boo hoo.
If an individual pushed the point, you might get a refund?
So far they’re not budging from offering me half of a refund (excl. delivery).
They’re still stating that the BSD of the Nightrider is too big; yes thanks Sherlock, we established that weeks ago, but failing to admit that they misled us and produced a product that was not what was claimed.
The T-monster is unavailable - they can’t simply find me one. There is only one source of manufacture.
The tyre they’re planning to try and sort will be ages away - very unlikely to be available before the T-monster.
I’m sure they’re also still reading this thread.
Nextie, just do the right thing. You f*ucked up here making a product that was not as you claimed.
Refund those who bought it for a purpose that you sold it and numerous times stated it was fine for (a Nightrider at 60PSI), and then change your website to the facts so nobody else makes the mistake of buying the rim for one of these carcass tyres (if they wish to run over 30PSI).
You’ve made by all accounts some great rims - and we agree that according to the spec you made them to they’re not at fault, but you’ve not made the product that you said you were making, that we wanted to buy.
I know for a fact that you’ve offered at least one full refund for the hookless one to a buyer who discovered that it wouldn’t work with the tyre they had, and that wasn’t even your fault as there were no claims of compatibility made.
Here it is your fault. You’ve made false claims to sell a product.
You may have missed one step of the fairy tale. The current company, producing the “light” versions of NR and KG (and quite possibly TA) are not the original company.
All currently selling versions are made by Innova, who are likely an order of magnitude (or more) larger than a company like Nextie. They also make custom tyres that are rebranded by a bunch of other companies, including Surly. I would not be at all surprised if the company that Nextie reaches out to (to make their new tire) is Innova, not least because they already have some expertise in this area. Just sayin’