That's a really loaded question. Any trailer that is aluminum composition will have a slightly higher deck height, although it will squish down when you fully load it. So that eliminates aluminum framed trailers. There are various ways to mount the suspension, and you can even have a slightly sloped trailer(down towards the front) to help you out. Both will help. You can even go lower than 34-36" if you put steel wheel wells around the wheels. It's pretty rare to see a trailer like that though. The wheel wells stick up quite a bit above the deck. The deck might be 26" off the ground or so. Kind of like this trailer:
2009 TRAIL KING TK90ES Drop Deck For Sale At TruckPaper.com
But lower and with wheel wells. I'm pretty sure someone on here had a trailer like that.
Don't buy the advertised height, that could be with the suspension dumped or something. The guy could even lower the landing gear and measure it that way. The only proper way is with the suspension loaded and hooked to a truck.
Although I didn't answer your question, these are the variables you have to look for. If a company doesn't offer 17.5 tires, etc... then don't bother with them.
For aluminum look into MAC or Chaparral. Steel frame I'd look into Doonan or maybe Landoll.