I agree with Loggy...... if you are going with a 38" swamped barrel for deer hunting with roundballs, do yourself a favor now and skip the .50 and get yourself a C weight Colerain in .54. Maybe it's just me but I don't like a .50 roundball gun.....at all.
That particular Colerain 38" .54 has great balance, more punch, in a probably 8lb finished rifle.
I personally gravitate toward longer rifle barrels......but have experience with that 38" .54, and one of my hunting buddy's has that same barrel and in an Isaac Haines modeled gun to boot. He has had terrific success with it and you couldn't pry that rifle out of his hands.
My personal hunting rifles right now have 44" and 47 1/4" barrels. Don't fear length with a properly chosen swamped profile and caliber.
Do a little homework on barrel lengths, profiles, weight and how they relate to a finished rifle weight and balance. Longer doesn't always mean heavier or nose heavy.
Oh and I don't know who told you that "The Haines rifles were 38".....? True to a point in that one very famous rifle of his that you see in all the books is a 38" barrel (that one a .60 cal), but of the 3 others that I can find in a couple of my reference books here on my desk I see a 44"/.56 cal, a 47"/ .57 cal, and a 45"/ .50
So truly......go with a length and caliber that you prefer, not because of a notion that a majority of a builders guns were a particular length. Not true.