Yeah, I believe the practical maximum for a 10 gallon batch in a 10 gallon tun is 1.060 or thereabouts. I don't think the round coolers normally come in sizes larger than 10 gallons, so that's really your only choice if you want to use the false bottom with it. I have a 12" domed false bottom in my 10 gallon round cooler mash tun and it works beautifully. You might consider having a round cooler shipped to you instead of buying there if they're so expensive there. If you're trying for higher gravity 10 gallon batches then you're looking at a rectangular cooler with a manifold. The false bottom won't fit properly in a rectangular cooler.
The only thing more asinine than stupid rules is the enforcement of rules simply because they are the rules.