Nate, completely sealing a trailer is doable but it can definitely take some time to get right with good seals, especially on a home build. You know I still don't have a lid on my trailer. Yes it gets dusty. Cruiserfest last year was some of the worst dust build up I've had in the trailer. EVERYTHING was covered.
.
However, without a lid I've been able to keep my gear mostly dust free with the use of containers. The containers also helps me organize the gear in the trailer too. I'm not using anything fancy but just some bins I found at Walmart. The lids clip closed and I've even run a wire tie through them a couple times to make sure they don't come open on their own. As is, the bins do ok keeping dust out but I used some thin foam weather stripping around the lip of the lid to create a better seal. This has been really effective.
This is the best photo I have of the bins. They're black with the yellow lids you can see here. They nest with each other nicely so they stack well and are easy to lash down.
.
The other thing that has been a huge help in keeping dust out of clothing (or whatever else) is my Tepui gear bags. I had these in the bed of the truck and in the trailer during Cruiserfest when the dust was into everyone's gear. I never had any dust get into these bags. These have become my favorite piece of gear. Not exactly cheap bags but worth every penny.
.
.
But if you end up building a lid with a good seal and seal up your tailgate, it will help a lot. Combine that with some of these bins or bags and you should be able to keep dust out of just about all of your gear inside the trailer.