1. What is "excessive"? 1.5V? 1.1V? anything over 1.000V? ...


Anything over 1.0v is excessive.

2. The cathode voltage for each tube is given as 3.5V. Clearly if one of
them is way off, it's pretty much the one that should be replaced. What
if
they're both close but the difference is a little over 1.0V? Should I
just
replace both?


Can't help you there.

3. Should I just replace all 4 tubes in the circuit? There's also a
rectifier tube whose output is filtered by a couple of 10 uF capacitors
[actually three sections of a single capacitor) and a 6H choke. How much
60/120 Hz ripple on the DC output of the power supply would suggest that
the
tube and/or the capacitors should be replaced too?


Have you tested the tubes? How much are replacements? If they're cheap then
it wouldn't hurt to replace them to see if it helps. Don't forget to change
out any electrolytic capacitors too.


4. The really hard question: Am I still trying to polish a turd and
should
just replace all of the electronics with a good quality IC-based Wein
Bridge
using the dual variable capacitors as the basis for this?


I would absolutely attempt to restore function of the original instrument,
vacuum tubes can still perform very well and that oscillator will provide
excellent performance once you get it going.