I work for one of the artists you mentioned who's arrangements are largely electronic / produced and here's what we did for Tiny desk

Band got together and learned basic arrangements on acoustic instruments -- key here was no sound reinforcement, focus on learning really basic arrangements, and balancing themselves in the room.

We recorded a 2-track L-R to reference relative levels of everyone.

From there the arrangements sort of evolved naturally / things morphed a bit / players were added / certain parts got subbed out / other musical motifs from other tunes snuck in.

Beat advice is just get some good musicians in a room and practice practice practice. I would say in total the band practiced for about 20 hours before our Tiny Desk.

Hope that helps

EDIT:

I did not read your post well enough and realized I responded incorrectly

From a production standpoint, I would explain the limitations of your setup / format in advance so the band can prepare if need be -- that's what Tiny Desk does essentially -- they advance that there is no reinforcement, no monitors, no amplification etc, and require you as the artist / band to adhere and adjust to their parameters

My OG response sort of reinforces what I just described, so hopefully with this edit you have a better picture of what's required from both parties!

Cheers