my initial plan was to make a 3d printed full enclosure for the board and the transverter, but after considering all pros and cons, I decided to to build metal case. The work is still "in progress", although has been stalled by a combination of problems with USB pigtail, lack of time and procrastination on my side. I took some pictures, and jynik was kind enough to upload them to imgur: https://imgur.com/a/Mkx3K
After replacing the connector I decided that had enough fun doing it once, and designed a 3D printed clamp to relieve the stress on the connector from cable crammed inside the case. It turned out to work really well. I can route and bend the cable as necessary to put the case together, and I don't need to worry about ripping the connector out of the board.
The most important thing that is holding me from finishing the build is a problem with finding a reasonably priced, working USB3 pigtail, with angled connector. The one in the pictures I bought on ebay, but it is of so poor quality, that the controller refuses to push any data through it (board enumerates, but the connection crashes as soon as I try to move any data. USB2 works fine, though).
To answer your question: if I still was going to make a 3d printed case, I'd add similar cable clamp to it. I wouldn't try to clamp the plug, as it should have some wiggle-space to adjust to the connector on the board. Stiff-mounted plug would only add stress to the connector, instead of reducing it.
The board does not heat too much in the area of the USB connector. Most of the heat is produced by the LMS chip, and you should make sure to leave some space around it for air circulation.