[Electronic M]

It sounds like your problem is that the video output tube heaters aren't lighting. Since the tubes test good that means the set is not supplying voltage to the heater pins of those tubes.

Caps usually have NOTHING to do with heater supply issues. To troubleshoot a heater supply problem you need 3 things that it sounds like you have. A brain, a working DMM, and a copy of the schematic. You don't need chassis pictures for this.

You need to measure the AC voltage across the tube heaters of the 2 tubes and trace their wiring. If the set uses a power transformer* (as ISTR reading it did) the heaters are wired in parallel. So either the heater feed wire that feeds both tubes failed, the heater ground connection failed (common on tubes mounted on printed circuit boards), or in the least likely case both sockets have open or damaged heater contacts. If you measure 6V across the heater pins at the socket the socket is bad. If you measure significantly less than 6V there take the probe that's on the grounded socket terminal and touch it to chassis ground...if then you get 6V your ground is open, if not keep one probe on chassis and trace the positive heater line to the solder points it connects to and measure voltage till you trace back to a point that gives 6V AC or you reach the heater winding of the power transformer (which ever comes first). Somewhere you will find a bad connection, bad wire, bad trace or open circuit.

How do you find the heater pins on the socket? The schematic will have symbols for the tubes. Locate the tubes on the schematic and locate the heaters of the tube they have this symbol (^) or this one (^^) on the schematic symbol of the tube. Most schematics put the socket pin number next to the wire connecting to the tube element (if not google for the tube datasheet and it will have that info).
The tube pin number on 7 and 9 pin tubes is counted up clockwise from the big gap (in octals it's counted from the bump on the Bakelite pin) between pins as seen from the bottom of the socket....(if you are looking from the top side of the socket where the tube inserts it's counterclockwise).
Sam's won't show you every wire on the schematic...the hot lead of the heater probably will go to an arrow with an X, Y or Z next to it. The power transformer will have a similar arrow with the same letter next to it. Heater wiring is electrically simple so to keep it from cluttering up an already complex schematic Sam's uses those arrows to indicate every arrow of that letter is electrically connected to every other arrow of that letter with some set of wires. (They do similar things with B+ wiring in most schematics except stuff from the late 40s early 50s).

*If the set is a transformerless series string heater set then there's a short bypassing current flow through those 2 heaters. In transformerless sets Sam's doesn't put the tube heaters on the tube symbols and instead clusters the tube heaters near the power cord to show how the series heaters are wired to simplify troubleshooting the heaters.