Hi Bob,
Don't waste your time with the Sovtek tube & kit, you can buy the real thing in Electroharmonix, 7591EH. I recently bought a quad, all matched,in Canada.
Yes, check for shorts with your meter. Also, replace all B+ caps with total removal of the originals (don't use the original capacitor terminals as tie points). The multi-section capacitors you bought are fine. They are attached with clamps that screw into the chassis and have a band to tighten them with. Most suppliers also have these clamps for sale. If in doubt, call them and ask.
Replace all the grid coupling capacitors before trying anything. Certainly before installing tubes! Use the proper axial capacitors, not the "orange drop" types that are radial capacitors. They will not fit in the same spot as the originals. Make sure all your new components fit and leads run exactly like the original ones did. Lead dress is important with tube amplifiers, and you can change the sound, hum levels and even oscillation some times if the parts don't sit the way they ought to.
You should be seeing B+ voltages, but they will all be too high without a load. Before powering up again, replace the existing rectifiers with silicon diodes. 1N4007 would work great, but you need to add some series resistance to drop the loaded voltage to its proper level as stated on the schematics. Just worry about the first voltage reading as the others depend on the loads that are on them. Set your variac to 120 VAC or to whatever the voltage in your area normally is.
After checking for shorts, etc, smell all the transformers. If you smell one that smells burnt - sweet, there is a high chance that transformer was damaged. Keep your eye on it - and any tubes if it is an output transformer. Look also for level differences between outputs if an output transformer smells bad.
If everything checks at this point in time, replace all the other coupling capacitors and check the resistors for proper resistance. Replace those that are out of spec. If replacing a resistor, make certain that the replacement can handle the voltages in that amplifier. Obviously a grid resistor, and most cathode resistors will never see anything above 100 VDC, but the others may well see a lot more, like full B+. Some resistors have breakdown ratings as low as 50 VDC! Check, be sure.
-Chris