That's some pretty thorough testing you've done so far, especially with
testing the filament winding open and under load. It think it's safe to
say the filament is good, and either the HV section has an issue or the
magnetron is just bad.
Testing the HV part is a little trickier. Do you have a way to safely test
the HV output from the doubler? If not, just skip this.
Next step would be swap parts, starting with the cheap ones. Swap the
cap with a new or known good one, then try the diode. If that doesn't
help, you probably have a bad magnetron, which may or may not be worth
replacing.
This has some pointers, which you've probably seen already
http://www.repairfaq.org/REPAIR/F_micfaq5.html#MICFAQ_001
It's a good doc for learning the concepts or experimenting at home, but
sort of pointless for real repair work, where speed matters. For example,
in a real shop, nobody takes the time to build a test jig for diodes. That
would cost more than just replacing it, even if that's not the problem.
Tapping into the filament with resistors seems weird too, since most
places have a current meter, and if you're confirmed the HV section is
good anyways, there's nothing left to replace but the magnetron, so
proving that the filament resistance is 4% out of spec doesn't even
accomplish anything anyways.