OK, it's getting more interesting. I'm not sure why I decided to try the DCmV range but I did. It was spot on. So it seems unlikely that U1 is bad given the proper current draw and the accurate measurements in DC mV, mA, uA and A. The VAC range is way off (based on testing a wall outlet). The diode, continuity and resistance are also way off. It's really seeming like I should have a single bad part somewhere in the path between the positive input and the IC. I'm not seeing any board damage even on close inspection but I might still be missing something (well clearly missing something since it doesn't work).
Incidentally, I found the Fluke 8025B service manual seems like it's probably closer to the correct schematic for this meter. The Fluke 27 service manual I found seems to be from the final version of the meter, not this earlier iteration.
Incidentally, I find it interesting that the 8025B had a third fuse. In addition to the two buss fuses, it also has a cheaper glass fuse in series with the low current fuse. I guess the idea was the cheap one goes in most cases but the pricey one is still there if the poop hits the fan.