I test my lawn and garden wheels in a big tub of water, bigger than the wheel. Leaks are usually very obvious, air bubbling out. I've had the trifecta, leaks through the side wall (trash), leaks from punctures (usually from bits of fence wire), leaks around the valve stem. Leaking valve cores are easily replaced. I've seen some tire stores have a big lever to hold large tires under the water.
Yeah, the smaller the wheel, the harder it is to change a tire. I have some with bolted together rims that are very easy to change the tires & tubes. On some equipment it costs about the same to buy a whole new wheel with tire vs just a tire. My local farm & home store gets their lawn and garden tires tightly bundled together so they are quite deformed. That makes it even harder to install and inflate. I won't buy those anymore.