Well, yes - LOTS of thoughts and you will get even more opinions! But here are my thoughts ...
Barrel profile would be caliber dependent, i.e., to me you could go with a 7/8" straight profile barrel in a 45 or lesser caliber bore. I personally find the 50s on straight profiles to be TOO MUCH forward barrel weight. It's OK for a few shots, but not a string of them. Once you need to start using 'muscle' to hold the rifle, you're done for. Now there are execptions there, as I have a lowly 40-cal rifle bore but of loooong 44" barrel in a 'swamped' profile, and that hangs really nice! Usually and offhand gun with open sights has more drop than a scoped rifle. I find the early Flintlock school rifles to have adequate drop, i.e., think rifles like the Kibler Colonial rifle.
You do want the weight forward, where typically your balance point would be by the rear sight or just behind the ramrod rear entry pipe, but for a target gun that can balance go to that pipe if not more forward.
However, since I shoot offhand exclusively, there is MORE to offhand shooting than just the rifle itself, in fact I would rate it LAST on this list of everything I've added here. Now I do shoot modern highpower shootingoffhand to 200-yards weekly, but I also shoot black powder cartridge Schuetzen rifles, weighing to 14-pounds, out to 200-yards routinely. I am now practicing with my 50-cal flint longrifle out to 100-yards weekly, for the upcoming NE Flintlock contest to be held in Maine this Summer. And case in point to where I say your rifle choice per se isn't the biggest asset here for offhand shooting competence, at the weekly Winter milsurp shoots, I shot 3 different rifles, one over 150-years old, and I still placed amongst the top scorers,
Offhand Shooting Reading - For me, I have found the BEST articles/info to be from numerous sources, like that by the famed barrrel maker Harry Pope on offhand shooting - see link here:
https://www.issa-schuetzen.org/off-hand-rifle-shooting.html Harry was of slight build, barely weighing 120-pounds, yet he shot a 14-pound rifle and one record group shot at 200-yards offhand,
with black powder loads no less, still stands to this day!
Also the books on highpower shooting by M/Sgt Jim 'Jarhead' Owens - see link here:
https://jarheadtop.com/ In particular, his books and info on
aiming and establishing the
Natural Point of Aim (NPA) are worth their weight in gold. I've taken shooters who 'think' they know how to shoot, teach them to correctly establish their NPA
before they shoot and they routinely add 10-points to their score!
Now worldwide, the generally accepted 'Bible' on competitive shooting is the book by A.A. Yur’yev called
Competitive Shooting: Techniques and Training for Rifle, Pistol, and Running Game Target Shooting.
Offhand Practice - I'd recommend 3 things before you even hit the range with your flintlock.
(1) Get a good quality, pre-charged, gas, or single pump air pellet rifle and shoot in your basement or garage constantly. Practice with a purpose! The Daisy 853, available refurbished for $100, from the Civilian Marksmanship Program (CMP), is a phenomenal value to 'learn' how to really shoot. It will group better than you can. See link here:
https://thecmp.org/sales-and-service/sporter-air-rifles/
(2) Practice picking up your flint rifle, with a wooden flint in the jaws, a few times a week and cheeking it and getting into your offhand stance until you can do it
and be on target in you sleep. Your stance is crucial to good offhand shooting for a string of shots, again - the NPA. Anyone can hold a rifle and shoot 1 or 2 good shots ... but try for 10 or 20 in a row, like we offhand shooters do. If you have a good quality lock, do some dry firing with the wooden flint - stay on target and focus. At the range with BP arms, I see too many drop their musket/rifle right at the shot to see if they hit ...
which always causes a miss ...
(3) All your focus MUST be on that front sight! I am left-handed, but do own and shoot RH'd black powdah arms and I have never, ever, evah seen the pan flash from RH'd firelocks, flint or matchlocks! Why? Again ...
because I'm not looking there ... as all my focus in consistently and completely on that front sight THROUGH the shot and into the folllow-through. Learn to focus ALL the way through the shot, learn to call your shots - like that went 'high left' - as that means YOU knew where the front sight was as the trigger broke.
Learn the 'proper' way to shoot sir and you can shoot anything! Good shooting is quite simply eliminating 'bad shots'. For in the end - NOTHING ... nothing beats trigger time'! And that does NOT have to be live fire with firelocks to achieve it ...