While it is true that signal processing was a fledgling art at the time that was recorded and had little impact on the sound, you still cannot discount the natural proximity effect of microphone placement and some simple desk eq.
I like the EMAD heads and have had good success with them when I have used them. The tone of the drum becomes a bit deeper and the punch has been increased while the attack seems a little more wet. I would imagine Charlie was using coated heads back then but replicating his set-up may not produce the sound you want.
It is also true that the kick will sound different to you from a player's position than it will out front and there is no way around that except for monitoring. When you include monitors, then the same sound you are sending the audience comes back to you.
George Lawrence has a Radio King kick drum that he slapped a PS3 coated batter head with whatever reso head was on it and it sounded every bit as good as Charlie's kick. It was outstanding with a ton of low end and oomph abd really impressive. I immediately tried PS3 coated heads on a 20-22-24 Slingerland kicks (from 1962 to the late 70's), a 22" Ludwig B/O kick and a 20" Premier and did not like it on any of them. It depends on the drum and the space in which you are listening to it.
I don't have a copy of Honky Tonk Women to assess, but I recall thinking that the sustain of the note on "one" is very different than the "and of 3" and the "and of 4" and wondered why that is. Is it possible that Charlie played out of the kick on the down beat and into the drum on the two off beats? If so, I am very impressed with that bit of musicality and technique. Perhaps I don't recall this correctly though.