This sounds like a pretty great project. You’re probably familiar with PARKing Day: http://parkingday.org/ I don’t know if anyone has ever done a moving parklet for that event or not, but it’s a great idea. If you follow some of the links from the main site to the individual city sites you should be able to find a bunch of photos and inspiration.
I think one of the biggest challenge moving from the dumpster to a trailer will be limited soil depth. You’ll have to build or securely install containers for your plant material. As with any containerized plants, consider the need for irrigation and drainage. Also think about the expected longevity of the installation. PARKing day is a one-day event, whereas it sounds like the dumpster/trailers may have a longer display time. That may influence both plant choices, materials, and cost. It would be cool to calculate the carbon footprint of transporting your parklet to your various locations, and see how much vegetation it would take to offset it.
Do you mind sharing how your firm got this work? Did the Navy request this, or is it part of a larger project?