[joeq]

one way have your cake and keep it organic too would be to get a looper

pound on the wood of your acoustic for a few bars and loop that

or sit for a minute at your stomp box, get it going and then stand up to play

it will give you whatever rhythm you set, it will go indefinitely just like a drum machine, but it won't be as electronic sounding

you could overlay string scratches, mouth percussion, even choral licks
You could just use it for a beat or get as fancy with it as you want, a decent looper should let you drop parts in and out, etc

the best part is, the audience gets to see you put it together in real time