Being someone who lives in the tropics... I don't see any problem. You might want to be a bit more selective in which
trees you bury, though. Generally speaking, for the tropics, you assume twice as much organic material needs to be added, due to how rapid things break down. You also have to factor in there is NO season where things "rest".
Think of yourself as having 3 times as long a season, and you are about right. This is because, even in a place like Florida, you do have a time when the trees lose their leaves, or at least, are chilled. Here in the tropics, we don't, unless it is due to a dry season, like in Guanacaste.
The big thing here is charcoal, it will last a long time, much longer than wood buried. But, I think I would use hugelkulture as well. We have so much wood waste in the form of sawdust and wood shavings, as well as lots of sheep manure, that we don't bother. We just pile it on, let it rest for a bit, and then plant. My system that seems to work pretty well is if I need a bed, break up the soil a bit with a garden fork (just a quick turning of the sod over), bury it in an inch of sheep droppings, or more, then put sawdust mulch on that. Then I plant on that. Sometimes I don't use the mulch, just broadcast lettuce, broccoli, radish, onion seeds and scratch the surface with a hoe, and then wait.
I might not even have to turn over the sod, I could probably bury it, but I like the exercise - and I collect a few worms to go fishing. lol