We used to use the blitter for that and then there was a memory location to write to to initiate execution of what was uploaded. The Jaguar developer docs are available online if you haven't seen them.

Once the GPU or the DSP was running. You could then chain overlays together by running to a location in the GPU itself from which you called the blitter to upload the next segment and then you could just jump to its first instruction. I believe later compilers enabled just running the GPU from main RAM but it has been decades.

It was unwittingly extremely useful mental preparation for programming in cuda a decade later.

Ah yes, I'm more worried about the actual limits of what the combination of Linux + the initramfs can let us do (Memory wise, mostly).

In theory it should be feasible but I'm not too sure how you'd "adapt" the way of doing things within Linux; the environment is very limited and I can't think of a way to cleanly make the Tom more "accessible" (While again, Tom is already executing the object lists to drive the Linux console). Doesn't help that it'd need additional afterthought not to trip it up with one of the many hardware erratas both Tom & Jerry had...