Here's a very simple idea for the bass drum that I've known about for a long time but didn't start really working on until recently.
When one plays a fairly open (non-muffled) bass drum, we can play it two ways. We can play off the drum getting an open ringing tone, much the same way we tend to play a drum with our hands. We can also play into the drum. This will shorten the duration of the note and also make the drum's pitch higher. (I noticed I can raise the pitch of my drum by almost a minor 3rd. Lower pitched drums may have even more range.)
So I finally decided to make use of these different sounds. I started by playing any sort of bossa pattern and playing this in the bass drum:
The +s mean shoving the bass drum beater into the head, (make sure the beater doesn't "buzz" while doing this. I find it helps to play this part heel up) and the os are playing off the drum head. When I was working on playing off the head I would often imagine the beater was returning to it's "normal" position away from the drum head, and the pedal board was forcing my foot up. I also feel playing this part heel down helps.
I call this Pseudo Surdo because the open bass drum on beat 3 sort of imitates the open surdo sound found in lots of brazilian music. If this is too much at first, try it with only half notes on 1 and 3. This can feel sort of strange at first, so take your time.
Obviously there are lots of other applications for this. I've also been playing swing four on the bass drum and playing closed on 1 and 3 and open on 2 and 4. I've also been messing around with some funk beats and working on changing the pitch of the bass drum within the beat.
This also might be a good exercise for you "Bass drum squashers" (as my teacher Jack Mouse once described drummers who only play into the bass drum head) because it forces us to be very conscious of how we're playing the drum.
Elvin used the open and closed bass drum sounds to great effect, almost getting a quasi tabla vibe. Here's an example of that from the late 70s.