Piedpiper : I agree that of course one can do both. I do suggest that once you know the condition of the software , its easier to make recomendations on spending one's money ... That will become evident later.
As for what to replace first , to me its a tie between the table and the arm. I am of the opinion the scoutmaster is about as revealing and flawed as 85-90% of the tables available and the same applies to all pivot/bearing tone-arms. My bias is air bearing tables and tone-arms but that may not fly .
Other than AB's , for my money , make the leap to a Raven TT (either one) and a Frank Schroder's magnetic repelling Reference Arm with a Soundsmith's strain gauge cart w/its own PA included. That's about 28K to get to the point where you hear just about all that LPs have to offer-warts an all. That's why pristine records come into play.
Of course you can spend more much more but the Law of Deminishing Returns overtakes you. Other than that, I would carefully clean all my connections , maybe apply a tweak or two to the scout, re-adjust the TA to spec's, demag the cart and system-at-large and enjoy , simply because what the father owns is pretty good sounding gear.
Then again, you can be crazed as I and buy a Maplenoll , a marriage made in heaven or ---- depending on one's commitment to the equipment. One of the most revealing and beautiful sounding rigs , when you get it spot on. Piedpiper would recommend air bearing ?