How about having a method where you can set up and run a full node on PC that you own, and once that's done you can have a pruned version of it, of the latest x blocks, and then have that transferred to what amethyst manages and have it always be in that pruned state from then on (new blocks in, old blocks out, of the latest x number of blocks constantly being updated).

This results and you having verified the whole blockchain on a PC, and after that initial big workload, you'd have a self verifiable pruned version always being updated on your phone.

I'm not sure if somebody did this already or not, or if it can be done I'm not sure, but it's a good compromise and sounds reasonable id imagine.