You are on the right track IMHO. Just be sure things are coming
up as they should, audio on the radio & HV on the TV.
Keep in mind the only bigger liar than a tube tester is a
politician ( both parties). They have there uses but its
best to deal with problems one at at time & not look for
miracle cures. You learn more that way anyhows. Many of the
low level tubes can be bought cheap also & they are the ones
that can bring a set from working OK to working like new.
Subbing a known good tube is the best checker.
We had a top-o-line B&K checker at the shop and never used it. It
was for the customers & the best salesman we had. Back
then there was 60%-90% mark up in tubes and that was for name
brand ones ! We did use a little checker. Plug in a tube & if
the light lights the filament was OK. Saved time on series filament
sets.
73 Zeno