Since you are right at the source, you can also opt out for a solid rubber tire (and a heavier rim/spokes) from amish. Won't be quite as giving to ride in rough terrain, but will hold up better.
I've bought inner tubes at Wal-Mart, and various local shops. Depends who has what I need when I need it... I'm lucky to live w/i 50 miles any direction of MAJOR towns/cities - several with more than one bike shop. One time, I went to 4 different places (that was a day I drove more than 200 miles) - no one had the size I needed and when I finally found one and got it put on - it had a hole in it! I found that I don't like the green slime ones - but understand we do a LOT of "cross country" type driving, have cockle burrs that go thru even mountain bike tires and I weigh more than 250 - meaning a lot of weight on those little aired tires - especially when it bounces thru a rut or ditch or even over an ant pile!! My sulky jog cart is getting rebuilt in OH, and will be coming home with the solid tires - just plain tired of having to deal with the aired up tires...
My Forecart is on heavy duty vehicle tires (car?) that are 13" and WIDE. So far, haven't had any problems with them - even with treating it like a marathon and cross country vehicle - trotting and galloping and "jumping" it over limbs on the ground at public trail riding places. The wheels on our farm wagon are VW wheels and I think they are 14" but are much narrower than the 4x4 type on the forecart - LOL. Still nothing like the ones on the wire cart wheels.