if you want a serious wheel and tire combo, you can try to find some 16" moped wheels. they're the same as 20" bicycle wheels. wrap those in pirelli mx75 tires. they make a 16x2.5 and a 16x3.
you can also use those tires on regular 20" bike wheels. they're dot rated "J" for 62mph and only 25-30 bucks each.
little bikes are a lot of fun. can't post a link from my phone, but check out my thread, "race bike, pit bike, or death trap."
What is the width of your 20" rims? Are they standard 1.75" wide rims?
You will have some empty space in to fill in the frame. You could add storage or batteries to drive an electric assist.
The cranks could be a tad shorter. Ive been looking at that empty space and I will have to do something. The bike will be for my little cousin. I will test ride but at 6' 225lbs it will be too small for me. Its just fun building stuff like this. Wider rims would be nice?