Welcome to the forum!...I know a bit about what you are looking for as I was in a similar boat. The largest issue that I think you face with a "production" gun is the Flintlock "lock" is often sketchy at best on production guns. I vastly prefur Flint as you are not rely on caps availability, and they just look "better" IMHO
I have a Pedersoli Frontier and it sparks just...."OK"...it is fairly accurate but it has a patent breech that can be a pain to clean, the architecture is not that great and I do get a flash in the pan with no ignition of main charge fairly often. I think the reliability of this rifle would improve by adding a white lighting touch hole, but it can be a pain to get parts for this rifle and I just can not recommend it.
I will suggest a slightly different path than what you asked for and you can decide:
Have you ever considered building a Jim Kibler kit? Kibler locks are fast and some of the hottest sparkers I have seen, also a white lighting touch hole comes standard and installed, all this quality will make a Kibler rifle a joy to hunt with and the American Made spare parts are readily available, but quality is so high that spares are likely not needed. Not to mention the architecture is truly drool worthy. A beginner builder can easily build a family heirloom quality rifle.
Now the kits are about $200 over the top $ price range you spoke of, this may be a deal breaker but the rifle you build will be worth North of $2000 if you do a nice job. Kibler kits are about the easiest to build that I know of.
The next question is: do you really need a .50 cal to hunt your intended game animal? The Kibler southern mountain rifle goes up to .45 cal and I would hunt deer with that but your mileage may vary. If you must have a .50 than Kibler offers a Colonial Rifle in .50, it is a much more heavy rifle, but if you hunt from a blind it may not be an issue at all.
My closing argument is that Flintlock "lock" quality is EVERYTHING when shooting and hunting, a poor lock makes a Flintlock rifle into a wall hanger.
Of course if you don't want a "kit" at any price?...wait for better advice than mine.