I use stop blocks to guide cuts, especially on the miter saw, but I've never used them on my router table. You could.
If you don't have a bit that will go deep enough did you look for a longer one? I buy a lot of router bits from MLCS. They are not the cheapest but are priced closer to the cheapest than the most expensive. I don't remember how deep I go for my P35s but it was easily within the 70 mm that my domino can do. I think it was more like 50mm which I think might be possible for a router. But your Taipan is a bigger gun.
If you cannot go all the way down with the router can you hog out most of the wood with the forstner bits and then take out the top 2 inches or so with a router to trim the sides straight? It won't do the corners for you or go the bottom of a really deep recess but it could make the upper part that is more visible nice and straight. Then you could finish with the chisel. I have to chisel the ends of my mortises too. Takes much more time but I don't know of another way to do it.
I used to own a benchtop mortiser. I sold it because it made kind of slopping looking mortises in my opinion. They use a square chisel with a drill bit in the center. I think a router makes a much nicer looking mortise and one I would be OK with on a gunstock. I used to use a router for mortises on furniture sometimes but it was slow and also it couldn't go as deep as I needed sometimes. But it made nice mortises. If you could find a woodworking shop with a big floor standing mortise machine I think it might do a decent job on this. But mortises for woodworking do not normally show so they might still be a little crude looking.