After another day of riding, the weakest points on the cartbike failed. A crash knocked off the front handlebars, they were luckily going unused, but it just shows that zip ties aren't that strong. Also, the plastic that held the crank set away from the bottom bracket collapsed, leaving that back at square one. After two rides to and from the hardware store, Clydefrog and I got the right brass washers (cheaper than stainless steel, and thicker), and finally resolved this problem, though another spritz of lube was necessary.
Back to square one.
Only one of these was the right size (it was the big one.) Measuring is important!