I'd plug away and finish replacing capacitors, and then worry about the rest.
Don't forget the electrolytics. I usually do them first, since the rest of the TV is pretty irrelevant if you have a crippled power supply. It would spoil your day if a filter croaks and burns up your power transformer.
A little dripped wax under a flyback is common and not a horrible sign in itself. I have sets in that condition which play reliably.
The HOT lead may be ugly, but it's working well enough to display a full raster. Like the dirty safety glass, I'd leave it until later. Once you have a sharp, brilliant picture with strong audio, you can worry about such details.
Regarding new non-polarized caps, to make life simple I usually buy everything with a 630V voltage rating even if the original was rated lower (200V, 400V, whatever). When manufacturers were ordering in huge quantities, they could save money by using the lowest-rated cap that worked in a given circuit. You are not buying in bulk and a cost difference of one or two pennies is not worth your attention.
Have fun! By coincidence, I recently got a couple of 1957-1958 sets (one RCA, one Philco) and both have triple speakers. They're not in a condition to compare, but I suspect RCA might win a Pepsi challenge, as it has a crossover network with tweeters & woofer, not just three speakers wired in parallel.
Let me know if you're still missing a schematic page. I can download many Sams for free via the local library subscription.
Phil Nelson
Phil's Old Radios
http://antiqueradio.org/index.html