I’ve given the brakes a good bleed using the shimano yellow plastic block. The problem still persists.
Is the solution to use a slimmer block to move the Pistons further out at rest?
Does it matter that I’m bleeding with the lever bite screw on it’s furthest from the bar position?

What model brakes?
Most models have the lever position adjustment, but only the higher spec ones have bite point adjustment, make sure (if you have it) that it is screwed all the way out before trying another bleed.
Lever position adjustment shouldn’t make any difference.

Old style deore that can’t use the funnel.

I filed the yellow bleed block down from 10mm to approx 9.3mm. Made a big difference to level feel/travel.

Yes. But also sounds like you still have air in the system, probably at the caliper

Try bleeding from the caliper up to the levers.
That way any air is going to rise with the fluid.