I have quite a bit of experience with fabricating from ABS. I looked up a photo of the Dolomiti top box, and it would be a lot easier to just build a simple box out of ABS and place that inside the top box like an insert, rather than trying to thermoform ABS to conform to the inside of the box using a heat gun.
Solvent bonded ABS is very strong, and an insert box made from something like .125" ABS sheet should make a nice rigid box liner that would be easy to remove. If you make it to be a close fit for the inside dimensions of the box, you won't really need to secure it with velcro. You can use something like 3M Super 77 spray adhesive to bond the carpet to the inside of the insert box.
TAP Plastics sells a wide variety of ABS in different sheet sizes and thicknesses. The best solvent for bonding ABS is Weld On 2354; if you do a proper job bonding the joints in the box, it'll even be watertight. If you want to go all out, you can actually weld ABS using a soldering iron.
This is a tool tube I made from sheets of ABS. It started off as just simple sheets, with the edges reinforced with 1/16" aluminum angle:
Here is the box after the edges were solvent bonded, welded, and mechanically fastened:
And here's the finished product:
There's probably about 10 pounds worth of tools and other crap in the toolbox, and it's held together now for at least 60 or 70 thousand miles.
