It's been a while since I've been subjected to that sound... but from memory... it sounded like the toms were tuned a 4th apart, with the bottom head being a 5th below the top head... rather ringy, sort of a "Bonzo-esque jazz tuning", that doesn't 'ring' quite as long.
The "reverb" thing can be created in a bunch of different ways... the easiest will probably be to just rent an AMS RMX-16 and use the "Non-Lin 2" reverb patch [which legend holds was created to recreate the 'Huge Paycheck' [Hugh Padgham] drum reverbs.
The "Non Linear 2" setting in
the Kurzweil KSP-8 is pretty damn close to the one in the AMS... and the KSP-8 is way less expensive, and
way more reliable.
In lieu of that... put a bunch of mics around a rather large room with a high ceiling... trigger a gate off of each tom/drum that will open the "far" mic that sounds best with each drum. You'll probably want like a 10-12ms delay on the trigger feed to allow the front of the drum to come through without the reverb getting in the way of the initial "whack".
It sounds like
a Drawmer DS-201 gate was employed as the 'reverb' seems to hold then quickly ramp down [as opposed to just turning off, but it's a damn quick ramp... something that I've only heard the Drawmer do well]. Then compress the living snot out of the reverb, and blend to taste.
Take none of the above as any form of 'gospel truth'... but [from memory] that's kind of a 'disection' of what I remember hearing with those. I could be a million and a half miles off...
Best of luck with it.