First I must compliment you on the overall finish. I know you struggled with some parts, but the presentation is outstanding!
The customised pickguard (whilst I'm not a steampunker ) looks great and the abalone top dome knobs work really well with whole colour scheme.

And I'll echo what Simon was saying about the neck and nut, but add a bit as well. From my experience, you can generally take off 1-1.5 mm of the apex without getting into problems with stability or interfering with the truss rod. And it's worth noting that 1-1.5 mm is a lot when it comes to how it feels in your hand.

However I share the same position as Simon in that a lot of the feel of a neck profile comes from the shoulder, not necessarily the overall depth (if that makes sense). I think a bigger change in how it feels can be achieved by sanding the shoulders and requires less "calculation" than taking down the neck thickness. And, as Simon mentioned, you can "eyeball it" and just go with what feels right.
Re-profiling can make a huge difference between a guitar that you want to play and a guitar that you feel obligated to play just because you made it.

I'm sure you can find an appropriate Tusq nut that would work for that neck. I've fitted Tusq nuts on several strats without issue (both Fender and ones I've built). And there's nothing wrong with shimming if it's done correctly. I use timber veneer, and once it's fitted and glued, it's simply an extension of the neck nut slot. Avoid using paper or cardboard though IMO.
Also, if the original plastic nut provides the right height, use it! At least for the interim. Yes, nut material is not insignificant, but a plastic nut is not instantly going to make a good instrument sound like crap. The tone of an electric guitar is far greater than just the sum of its parts. There are just so many variables, most of all beginning with the player.

Congratulations on completing your build. Good work!