47uF should swap for 50 just fine. Most lytics of that era were -50%/+100% tolerance. Even some of the more finicky circuits should not mind the roughly 6% difference there.

In the late 50's-mid 70's the 'old' standard value system of caps phased out. The values used to be 1,2,3,4,5,6,7 (maybe more), but changed to 1,2.2,2.5,3.3,4.7,6.8,8.2 (all numbers were available in various powers of 10).

In radios and the audio and PS sections of TVs go with the nearest modern value and everything should be fine. In other circuits of TVs that may apply with the caveat of if everything else checks out, but it should work better than it is, try to better approximate the original values....

If I'm replacing say an 80uF lytic and I don't have anything bigger than a 47u at the needed voltage I usually put a 33 in parallel with a 47 to get 80. If you keep a good selection on .00x and.000x caps it is easy to get a more exact replacement for most odd ball papers through parallel connection.

Looks like I'm going to be subbing the 80uF 475V caps with 100uF 600V caps.

I want to replace all the electrolytic capacitors before I prod anything else. It's working this well on mostly original lytics? New ones could make all the difference in the world.

That depends.... I have a Heathkit C3 cap tester that can test for leakage at up to 450V and capacitance from the pF range up to 2000uF, and have tested many caps with it in many sets. Pre-1960 stuff has a ~90% failure rate, but post 1960 stuff often has less than a 10% failure rate on lytics. It is not uncommon to find period lytics and many of the tubuars in a set like that still testing and working like a new cap...When they test good I leave them.
That set I don't think I tested anything but the PS doubler lytics and some tubulars since it did not act like it had bad PS caps.

After I replaced C6, one of the many electrolytic caps in the set, it made a huge improvement on image stability.

Also C5, the vertical section cap is leaking. I learned a long time ago to look around their contacts where they go in to the cap, and if it has white cruddies the cap is bad.

C5 has a lot of the white cruddies going on.

Let's discuss the Vertical Integrators.

Can anyone tell me how I would go about constructing these, or sourcing replacements? They've been mentioned to me multiple times, and I have seen it in other places, they are something I would like to know how to build, and what I would need to go pick up in order to replace them it becomes needed.

As far as I can tell; Three Capacitors tied to one common connection hooked in with two resistors in series.

http://boxcarcabin.com/integrator.html

I'm still learning how to do bigger repairs and understand a wider variety of parts.

Minor quibble, but that would be 2.7.
(There's also a 3.9 and a 5.6 in there.)

There are no integrators in this chassis.

Excellent, one less thing to worry about having to chase my tail after then. I suppose it's down to Resistors and Electrolyrics now!

For going by memory and my normal parts source only stocking 1, 2.2, 3.3, and 4.7 flavors of film caps I'm glad that was all I had wrong....