Hello.
Burke's right, I should have read and considered the end of your post too.
I've been playing percussion in several bands for several years, latin and non-latin music (rock, soul, jazz, funk, bossa nova, « chanson française », Caribbean music).
At my humble level, I think the 'classic' tumbao fits in a lot of situations, either 'straight' and classic like in Santana's
Evil ways or Steely Dan's
Do it again, or 'doubled' like in the Rolling Stones'
Sympathy for the devil or the Doobie Brothers'
Long train running (please excuse my lack of vocabulary, but you'll all understand what I mean here by 'doubled' since you certainly all know these tunes).
But you'll certainly get tired and bored (and your band mates too) if you play only tumbao along.
You can play other stuff, according to the song played, to diversify and enrich the playing. Another rhythm (the conga part in Marvin Gaye's
Inner city blues) works great for soul or funk tunes for instance.
I try sometimes to play some batá patterns on 2 or 3 congas if it fits with the tune we're playing.
A bolero on congas or a martillo on the bongó are efficient on slow tunes and ballads. I play the bolero for instance on 2 Pink Floyd songs we cover (
Wish you were here and
Comfortably numb). I like to play the martillo on this tune :
https://www.youtube.com/watch?v=K1J04ugcdi8.
I sometimes invent my own patterns too if I think they fit to the music. As long as my band mates (some of them being very long time friends, and good musicians) keep smiling while playing and don't glare at me, I know it's allright...
As Burke suggested, also use some other instruments : a bar chimes is very useful. Shakers, triangle and bells too. You can make you own shakers, which brings more fun than buying some from big companies. Shakers and triangle bring a lot of swing in a tune, either emphasizing the beat or the secong eighth note of every beat (the « and »). Or the upbeats only. Make some effects with the instruments (without showing off, of course), vary the instruments on a same tune to create some different atmospheres, etc.
Listen to the others, borrow some ideas from others. That's how you'll become inventive.
Just my 2 cents, hope it helps.