Too bad Fluke doesn't release schematics anymore.
I'm still learning how to read schematics, but I find the text based theory of operation information more valuable at this point of my knowledge level.
While there are no public schematics of the 170 series, the original Fluke 80 service manual does a good job of describing how the ohm measurement is done on the 400 ohm range. See page 2-3, section 2-8 of
http://assets.fluke.com/manuals/83_85_87smeng0500.pdfIn reading section 2-8, I suggest checking
i) switch/rotary switch contacts - give them a good IPA clean
ii) give the main IC a good examination using a 10x loupe to see if you can see any contamination
iii) maybe take a dental pick or sharp probe and drag it in between the main IC or ICs to possibly dislodge something that an IPA flush cannot?
iv) check the thick film resistor for dirt/contamination and measure the value especially the 1.0001k resistor
v) check the solder joints on the COM and V jack - I remember modemhead had some issues with this
PS. What revision board is your Fluke 177? I know they have a rev 12 and 15. The two are completely different internally.