I personally don't like to padd the inside of the kick. I use heads that have built in dampening (clear EMAD batter/Yamaha logo head ported which is a REMO with an internal ring very similar to the EVANS EQ3 ported reso). Soon I will change to (clear EMAD batter/EMAD reso) on my 22"x18" Maple Custom. On my late '60s Rogers 20"x14" I use a clear EMAD batter/EQ1 (with the air holes and muffling ring like the Genera Dry has).
That being said I tune the Reso higher than the batter say 4 hal turns above rinkles and the batter 2 Half turns above rinkle statuts. Basically an old Motown way of tuning because the higher bass notes travel farther and it really allows he tone of the shell to shine. I prefer actually to not have a port hole in the reso side because you loose like 20-30% of your tone. You get more volume with a port hole in a none micing situation But you loose some tone.
I like my kicks to sound like subs, Whooom! Open , jazzy with punch for droppin them bombs,
... Not thud. The most muffling I will use at this point will be the coated EMAD batter/EQ1 reso.
I have also feel that you should get rebound from you kick like you do from your toms. This comes by tightening the reso head not the batter (though I still use a medium tension on my kick batter). Not that these are all tunings for live situations I speak of the studio situation depends on a lot of variables that most time we the drummer will have nothing to do with. What the producer and engineer want is what they get unless you have proven yourself to be better than them in that situation. Like your name is Steve Jordan or something.
I currently don't have the money but, soon I will purchase the MAYS internal mic system with the AUDIX D6 and get the Yamaha Sub-Kick mic for the 808 rumble. At that point my head combo will be clear EMAD batter /EQ1 reso or clear EMAD batter / EQ2 (slotted grill) reso. Both of the resonant heads have internal rings.