I've seen BSA conversions that looked similar. I also believe that Parker Hale did these.
You're right. It's based on a P14/17. If your gunsmith gives you the all-clear, then you've probably got a $250 rifle that will feed, function and shoot as well or better than most $1,000 rifles made today. It also looks better, too, in my opinion.
These rifles respond very well to basic bedding, so if it were me, I would bed the action. You should definitely take the action out of the stock to check for cracks or oil-softening, anyway -- as well as hidden rust. You should do that before shooting it. Just put the stock in a vise, take the guard screws out and gently tap the top and bottom of the barrel with a mallet. That should loosen it enough to take it out by levering the barrel up and down to work the action out of the stock. If it is really stuck, then there could be a problem that should be diagnosed before you shoot it (like the possibility that some nimrod might have tried bedding it in the past and accidentally glued the whole thing together permanently).
You should also fix that broken piece of the stock because the rifle you have is about as good looking as a '17 gets... and I'm a fan of them.
With good bedding that leaves the action sitting solidly and stress-free in the stock, and a decent handload, I'd expect the sky to be the limit with that rifle. Surprisingly, those original 1917 barrels were darned good, even nearly 100 years later. The first one I ever used was on its last legs when I got it in 1997 and my gunsmith rechambered it to .300 Winchester Magnum. I was able to easily shoot under 1 m.o.a. with it and full power loads. I used it until it went to the great barrel factory in the sky around the year 2000 and then replaced it with an E.R. Shaw barrel, which I am still using to this day (and it shoots just as well).
Please keep us informed of your progress with this rifle.