With a few drummers, the lav seems to handle it. But when there are many drummers, you get vibration that sounds a bit like peaking, even though the levels are fine. It literally just shakes the walls.
Anyone have any experience with this?

It sound like you're over driving the microphone capsule itself.

Sounds like you need a microphone with a higher SPL range that can handle it.

I may be in trouble then because this is all I have. I may have to rely on the sound feed.
How can I position to the microphone itself to minimize vibration and get the best sound?
If it's wireless, will putting one further away from the drummers, but center on, help matters and reduce the load on the microphone?

My best results with a group of taiko drums have been, believe it or not, a microphone mounted on the camera. The object in this case is to capture the entire group's performance without singling out any drum in particular. If a lav is all you have, position it about 20 feet away from the group and you should be fine. If you have a mic on your camera, record that on your second channel as well. Watch your levels, average it so it's a tad lower than what you would "normally" record.

There are two cameras. I have two lavs as well as the two on-camera mics. The sound people are also recording but I don't want to take any chances.
If one of the lavs is further from the drummers as a backup, will there be any problem with the fact that it is wireless? It should be okay. We'll check it at the soundcheck.

If this is the drum I'm thinking of... some of those suckers are huge and get pretty f---ing loud. That would most likely overload a lav if close mic'd. FWIW, 'MY' 1st choice would be LD dynamics like a Sennheiser 421, but SD dynamics (like a 57 or 58) would certainly work, and they're relatively cheap. ($)
I agree, you should not rely solely on a PA feed or FOH recording. Especially with unknown SR equipment and personnel.

Absolutely agree with Rick.

A Senn 421U on a tall stand positioned above the "drum field" fed to a switchable inline attenuator (10/15/20 db or similar) and then into the recorder would do about as good a job as you could without going to extremes.

It was one of the original "kick drum" go to mics, and as such, can handle low freq transients as well as most anything.

In fact, for more choices, you might do a search on the music groups for "kick drum mics" and get more suggestions.

I used a 421 setup once to record the loudest event I'd ever attended. A weird thing with rocket cars, metal crushing robots, and lots of pyro.

Worked fine. But no mic will EVER get you an accurate recording of the real sound of a HUGE instantaneous wave like these events produce.

SO you do the best you can.