We live in Florida and take trips up to 4 nights long in the Everglades. Can you point me in the direction of the best quality/price "monsoon"-proof 3-4 person tent that will keep sleeping bags dry in heavy rains, for, say, <$200? Optimally something that wraps up small, probably has a "bathtub" bottom, and won't be full of little pin holes within a few years.
If you are talking about backpacking, then I don't think you'll have an easy time of it for the money you're able to spend. Occasionally, you might find a 3-4 persontent for around $100. Such tents are usually heavy and not likely to hold up well in the conditions you describe. Often they are not seam sealed, so you'd have apply the sealant yourself.
As I browse through the Campmor web site (they're my local outfitter), I see reasonable 3-4 person backpacker tents selling for $220-$250 minimum, with some prices as high as $500. Just so you understand, here are the trade-offs that you need to consider:
1) 3 season or 4 season? A 4 season tent is sturdier and more weatherproof (mostly wind/blizzard proof) but heavier and more expensive.
2) Ultralight? These tents are designed for the serious long distance backpacker, often made with special fabrics and titanium poles. They are usually 3 season tents because you have to sacrifice some sturdiness and weather resistance make them light. Also on the more expensive side.
3) Rain fly or single wall? Tents with rain flies are heavier, but tend to work better in damp conditions.
I have not backpacked in the extreme wet conditions that you describe, other than car camping in a large canvas tent that was extremely expensive, but practically bombproof. But based n your description, I would recommend a 3 season tent with a rain fly. Nearly all of these tents have fairly sturdy bathtub floors. You can increase the life of the floor by laying a groundsheet under your tent and never wearing anything other than socks when you're inside the tent. You shouldn't even bring shoes into your tent -- the grit you track in will increase the likelihood of perforating the floor.
Finally if you have a local outfitter whom you trust, I'd strongly recommend discussing your needs with them. Outfitters usually have a pretty good handle on the best equipment for their area, snd can often provide you with excellent advice.