turn of the century
I wish you the best in your pursuit of deer with the .327 Fed. Your comparison to the old 32-20 is interesting and I had not considered that. How popular or to what degree the 32-20 was used on deer at the turn of the century, versus the larger and more capable same class 38-40 and 44-40 is debatable. It likely was a case of "using the tools availabe" business again.
My train of thought was that the ..327 was akin to the the .30 US carbine round, bullet dia excluded of course. Certainly all of those cartridges are capable of taking deer, and of course have. I do not automatically consider any of them deer rounds, (.44 excluded I suppose) but it certainly has been done and it seems you are about to proceed accordingly yourself.
Shoot well, and be careful your high magnification scope does not entice you into shooting farther than the cartridge is capable of making clean kills. Personally, I'd limit my shots to under 100 yds and ideal broadside angles.
Best of luck!