I regularly put Marathons on Brompton rims with bare hands only. I.e., when you run into difficulties it is due deficiencies in the technique rather than tool shortage. Start putting tires on without tube in, nor tools. Yes you can take them off with no tools too. Then add tubes but make sure that you get air out completely. Roll them up. Unscrew the valve core when needed. If tubes are completely drained of air, it should not matter whether they are in or not, and so on.

Otherwise, yes, Tire Bead Jack helps, when you are sloppy, did not get air completely, want to save 15sec. Otherwise work on your technique. It will help you on the road. I had 3 Bromptons w/Marathons to service this summer. Yes, I put studded Schwalbes with bare hands too. It is not magic, but just rational deterministic process.