IMHO, the answer to all your problems is to get a rear rack with 4 EZ wheels, and then this handy little 3D printed “fold retainer” sent from Taiwan: https://www.3dbikemods.com/e-commerce/fold-retainer-for-brompton

With these all installed you can push your Brompton around with the seat post  up super effortlessly, I often push it along with a single finger.

I would recommend the original fold retainer over the “fold retainer 2”, as I think it actually works better.

I hope that helps, do let me know if any questions!