Cary, I believe you said this is your first TV, correct?
I also understand that you have neither substitute tubes, nor a tube checker, correct?
Next step is to dim your lights and verify that the plates on the 5U4 rectifier, the 6BG6 Horizontal Output, and the 6W4 Damper are not getting pink as this indicates something is badly wrong.
If any plates are glowing, turn the set off immediately.
Since you have not replaced any resistors, I assume that a resistance check will not be productive at the moment.
I cannot call the Sam's part numbers as the only schematic of the RA-112 is the Riders one at ETF which uses the factory numbers.
http://www.earlytelevision.org/tv_sc..._diagrams.html
However, I'm going to suggest that you measure all the resistance reading listed in Sam's from tube sockets, with the set unplugged. This will give practice for the next step and it might spot a pre-existing problem.
Make a Xerox of the two pages of Sam's and write down the resistance, at each point and color marking the ones that are off by more than 20%.
If no tube plates were getting too hot, your next step is to check the voltages that are shown in Sam's voltage chart.
Follow the same procedure of writing them down, again marking those 20% off in a different color.
James