My reasoning for making it not real healing was that cauterization isn't really healing (arguably it hinders proper healing because it creates burn scarring). It's only useful as a way to close a wound to prevent contamination and stop bleeding.
The bleeding thing isn't in baseline 5e that I could find (I looked after writing this) but I'm going to leave it in because I've seen a few homebrews that create it and I want to be clear. Unless I alter cauterize to be proper health, in which case it is kind of moot.
Welding constructs back together makes sense, but it sort of flies against the style of 5e to make such a narrow exception.
I ended up with everything except the 14th level Sapper feature finished yesterday, but it's not formatted yet. I'll figure that feature out and put the class up tomorrow and try to get some quick reviews for the other classes sometime next week (got plans this weekend).