Heavy duty rims are a PITA!

I think I know what you're writing about. I had the problem of the sprocket shifting from center. What I did was wrapped a brake cable around the hub between it and the sprocket. This kept the sprocket from deviating from center. Just wrap it in the gap. After the sprocket was installed and tightened down, I used hot glue to hold the cable in place. I have no sprocket problems due to off center sprocket now.

is there room for a flat blade screwdriver or something in the gap?

you could start to snug it, then stick the screwdriver in there and pry it around to where it needs to be.

When your sprockets starts to walk, note the high spots using wire method or simply eyeballing it. lay a 2x4 scrap on the sprocket teeth and tap with a hammer. The pine will protect the teeth but allow you to manipulate the sprocket.

every build we do has this same issue. what weve been doing has worked well.
1st depending on the space involved remove the dust cover and try and find a washer that fits over the hub .
2nd we use an engine lathe but a drill press and file will work to turn down the outside of the washer to fit the id of your sprocket most sprockets seem to have an id of 36.9 mm
a press fit works best but if it slips through take a punch and tap 3or4 spots around the edge to hold the washer in the sprocket during assembly.
3rd tap the washer into the sprocket then use ONLY four bolts at first to align the assembly,tighen only enough to get the rest of the bolts in.
we tighen in a rotating star pattern every other bolt .
as for thining the rubber i have been able to take a razor knife and split the rubber pucks along the "ply" lines but this has never lead to anything very flat .
it seems that wheels from the u.s. and tawain all need this adaptation the two ive built that are from china needed no washer at all? with those we just cut open a beer can and make two long strips of alum then wrap them around the hub and tape into place , however this method takes 5 and a half hands .
if all else fails measure hub and sprocket and post the size and i"ll cut you one and send it out
hope this helps good luck

Tighten the bolts slowly in a "star" pattern... I use a plastic hammer to tap it into place.
As you're tightening them, stop to make sure it's still straight before tightening them all the way.

Don't use the center hole to make sure it's on straight! Spin the wheel and look at the teeth!!!