Can’t lower action on G string to desired height - help troubleshooting?

[Bar Band Bassman]

So the shim only covers a narrow strip of the width of the neck pocket? Why not cut the shim to the exact width and length of your neck pocket? What tool did you use to cut the shim?

I shim only at the end because it tilts the neck back slightly. This allows me to raise the bridge saddle and offers the additional benefit of improving access to the lower (1st, 2nd, 3rd, etc.) frets.

BBB

 

[2F/2F]

Can’t physically go any lower.

You need more neck angle. The bass will play much better this way anyhow. Necks are supposed to 'lean" back from the body, not be parallel to it. None of your saddle intonation screws should be angled downward toward the bridge plate. They should be parallel at the lowest.

 

[TomB]

The narrow shim just ahead of the lower screws will likely reduce the amount of tweaking needed after. TB luthier @Turnaround has pretty well debunked the “shims cause ski jump” concern with some lengthy research documented in a thread here.
Edit: I see you did it already .
Oh, and I’ve made partial pocket shims with regular plastic window screen material to help stabilize a neck in a just slightly loose neck pocket situation. It did the trick.