I'd think that the problem with LFOs is that they don't make it easy to think about rhythm- they are tied to specific times. So it's a hard tool for that kind of work.

I've been enjoying tools like "euclidian rhythms" where you have a variety of sounds that all have a fundamental division of beat that they share but have differing numbers of beats-per-bar. I have a squarp pyramid sequencer that implements that quite well.

You might look in that direction if you haven't already.