How to clean focus screen on my (used) 1Ds Mk. III

I have a 1Ds Mk. III, and it has been used for the past few years.  Cosmetically, it is fine, but there is a lot of junk on the focus screen.  I carefully removed it and used a blower on it, but there is still a lot of dust plus some general residue.

Is there a way to clean it without ruining it?  I know it is an ultra-precise piece of plastic, so you cannot just wipe it (all the grooves and such).

Worth mentioning the humidity in my house is below 30%, so static is an issue for sure.

Any tips?

Thanks!