Today I was at a LBS here in Boston and saw a Kenda Flame 20x3" tire on a kids cruiser b*ke and thought it might be good for street. By squeezing the tire it felt like the sidewalls were really soft, like other cruiser tires. It looked about as wide as the 24x2.6 Kenda that came on my '06 DX, but I didn’t have it with me to directly compare.
It was briefly mentioned in this thread where it fit on a 2005 20" DX w/ 1/4" clearance on top and 1/8" on the side.
Go for the Big Apple 2.35. I’ve been riding one for almost a year now and highly recommend it. It’s smooth enough to do freestyle on, but has more volume to soften up drops. I think one of the main problems with wider tires on 20" rims is that BMX rims tend to be on the skinny side. I’m using an older Powerlite rim that measures about 38mm and it’s the widest rim I’ve been able to find so far. Any wider tire would need to be run at fairly high pressure to resist folding, essentially negating the extra bounce we’re trying to pick up by running fat tires.