Imagine 20,000+ cyclists all in one place. They don’t fit in one place. They use about a mile of road just to get packed in before the start. But at some point, not sure how they determine the start, the sag support starts along the route, at a speed of 10mph. Behind the trucks and buses the street is open to regular traffic. One year there was a group of riders that included some kids on 24" wheels. 36 miles is an awfully long way to maintain a speed of 10mph or better. My friends and I traded with them and rode their 24’s back up past the trucks and buses a couple of times, but it was inevitable that they weren’t going to be able to stay ahead. Not saying it can’t be done, especially with short cranks, but it would take a lot of fun out.
(DISCLAIMER: The last time I did the ride was, I think, in 1993. We cut out part of Brooklyn and all of Staten Island (and the ferry ride) by taking a shortcut over the Brooklyn Bridge. As seen in Vertigo’s avatar. Actually, they had changed the route to 42 miles several years before that, but we usually took a short diversion in Queens that cut off most of the “added” section and kept our ride around 36 miles.
It’s NYC streets, so you’re going to want to get comfortable riding on random pavement, some of which is pretty bad. Even some bricks or other unusual textures.
Dominant leg could be a factor; the equipment being at fault is unlikely. You just need to practice more on the other side. Everybody starts out with an easier direction of turning. At least you’re not Zoolander. Just practice making circles to the right. If your body knows how to do it one way, it can teach the other side how to duplicate that.
A 29" wheel should be able to do the ride without too much trouble. You’ll just have to keep moving, and not take any long breaks. In a crowd of 20,000, most of the riders are not super fit, and some are very ill-equipped to complete the ride. You’ll see every kind of person riding every kind of human-powered conveyance. If they do it like they did back when I was doing the ride, people with unusual cycles were invited to come to the front of the lineup, to get seen and to have a bit of a head start on the larger pack. After our first year (1985) we always made our way to the front, got to see some really interesting bikes/cycles, and got to start right at the front of the pack. The front was also limited to about 10mph by a bunch of ride marshals up there as well.
My ride of choice was my 45" Big Wheel. Cokers didn’t exist yet. 36 miles on a hard rubber tire? That’s a long way.
I got curious about what the ride is like today. It has gone through some changes over the years; for us it started out as being sponsored by American Youth Hostels, then there was a gap with a new route that included the Brooklyn Battery Tunnel. This website shows a map of the route. The route looks about the same as what my friends and I rode back in the day. You get to cross the 59th St. Bridge and the Varezzano Narrows Bridge, which are both big and pretty spectacular. And they list the ride size at 36,000 riders, and say it’s the biggest charity bike ride on Earth!
I found a scanned image from our first ride, in 1985. We’re riding down the FDR Drive toward the 59th St. Bridge. Notice that there is some climbing on the ride; from sea level up onto that and the even higher Verazzano Bridge. Oh, and look close. Note that the bridge in the picture is packed with bikes on top!