Scale everything x10, explode/paste in place etc, relocate circles so they'll intersect with 'walls' and not clash with other stuff, then pushpull circles through walls, intersect with context, delete unwanted edges and faces, hide edges you don't want to see, scale x0.1 etc gives this...
test-1.png
test-1.skp
PS: Purge you model before uploading, then it'd be 1/10 the size !
S