O.P. You are, essentially, correct in your thinking.
If you look at the way screwdrivers evolved, the best ones were always forged, and years ago most grinding wheels were big, so it wasn’t easy to hollow grind something.
I have many screwdrivers with forged tapered blades and they are exceptionally nice to use for some things, but generally the screw slots evolved over the years to suit the drivers (I’m thinking woodscrews here, with relatively shallow slots).
In engineering, screws were traditionally very hard, so if the driver wasn’t an exact fit it didn’t matter.
Gunsmithing was always different, and gunsmiths “turnscrews” were always a different tool to the engineers screwdriver. Shorter blades with hollow ground tips were the norm.
In your position, I would definitely be seeking hollow ground drivers. It’s frustrating that the automotive world doesn’t use them, but that’s the trouble being a specialist!
A suggestion. Start off by acquiring a set of a PB Swiss 1/4” bits. These are hollow ground as standard and a great place to start. Most modern European firearms use standard metric size screws, and these will fit just great. An example is shown below. If you feel a bit more flush, buy a few regular PB Swiss drivers. One of those is shown also.
If you work with slotted screws a lot, you will soon realise that just as nuts and bolts come in Imperial (inch) and Metric sizes, so do screw heads. You wouldn’t use a metric wrench on an SAE nut, so get a set of inch sized screwdrivers for inch sized screw heads. This is harder in hollow ground, but they are out there.
Personally, living in the U.K, I always keep my eyes open for old gunsmiths turnscrews. Many local gunsmiths have a cabinet full of used tools, and amongst the bullet moulds for .577”, the roll crimp tools for 16ga shotshells, and all the other oddment, I usually find a couple.
I seem to recall (trusting memory, always risky) that the stock bolt for a SMLE No.1 has a slot 1/2” wide (by a 1/16” I think). That”s not really screwdriver territory. If I encountered a screw that size on a machine I would use a 1/2 inch drive speeder with a 1/2 inch screwdriver bit. As you have probably found out however, that combination will not fit inside a stock.
The correct armourers tool was a brace with a long shaft, ground to fit that screw. They turn up from time to time, but many folks collect the tools now, which forces prices up.
Personally, I would grind a bit of tool steel to fit, and either drill a hole for a tommy bar, of file some flats and use a tap wrench. There”s a picture below of a similar tool I ground up. This was for a machine, but the same principle applies!