One problem you will run into is that most motorcycle and car tires are measured by the rim size.
Bike tires are measured by the approximate tread diameter.

So, a 20" car tire will be MUCH BIGGER than a 20" bicycle tire.

I'm not sure about mopeds. It is worth looking. My Schwinn 16x3" tires use a 12" rim, and will fit Moped tires which are an excellent upgrade, especially considering the Schwinn tires are getting hard to source.

Assuming you're using a 406mm rim, it should fit a 16" Moped tire, as well as moped tubes.

Shinko Moped SR714 - Amazon
Shinko Moped SR714 Front/Rear Tire - LeatherUp.com

I can't guarantee anything, but it might be worth trying out.

A year of heavy cargo use out of a tire doesn't sound bad. You'll have to weigh the differences of a lighter weight tire like the Kenda Kiniption above vs the heavier Moped tire.