I've already done drawings of exactly this idea. Here's the side view:
To make it look right, you need to use curves at the front and back - if you just draw straight lines from the original shape, they will look like hollows. I'll be happy to draw out the modified profile if you let me know you're interested.
As with the modified HF trailer PDF on the Widget page, the trailer will ride somewhat higher than the original (84" high excl roof vent) - though you can reduce that by flipping the axle. However the greater ride height means that you could increase the depth of the dropped footwell by a couple of inches for some more headroom, if you wanted.
The footwell of the Widget is a problem with the HF trailer, as this plan drawing shows:
The bottom half of the drawing shows the unmodifed HF trailer and you can see that the second cross-member cuts through the footwell. You really need to relocate that cross-member 8" further back, as shown in the top half of the drawing, which should be just a drilling operation.
To build a Widget within the 1450lb empty/1650lb laden of the weight estimate (and the HF doesn't leave you any spare), you're going to have to keep the weight down. 3/8" single-skin for the walls sounds fine, though you'll still need the framing to hold it straight, 3/4" for the floor is unnecessary (indeed you could go below 1/2" under the bunks). I'll let others say whether you can bend 1/4" for the roof.
Andrew