Here's a few more ideas:

1/Patching:

Right now while you've got the raw material on hand, cut a bunch of paper thin strips of each type of wood that you are using. And I mean paper thin!!- you'll be able to easily and rapidly shape these with a razor knife or even scissors!

Then when you sand through, cut a patch with scissors, glue it down, and lightly sand. The real thin area is hopefully localized and won't cause a problem. Or most likely the sanding through will make feather thin edges that will fair in well into a patch from below.

2/ Gaps:

You seem to have fairly regular design patterns - if you are lucky and have fairly regular gaps what about using these as part of the pattern? For example what would happen if you put a drop of black pigment in some glue and filler and spread it into the gap? Would it look interesting? Could you play with dark and light? Pretend shadows?

Others could help here better than I, but alternatively, is this not a prime candidate for a seal coat - in that it would put a skim of epoxy in all the gaps? Maybe repeat as necessary to get the fill you desire? Is cabosil filler or are microballoons as filler transparent? If not, multiple layers of seal coat in particular locations only, and then put on the cloth.

some thoughts for what they're worth:

-mick