[murphyv310]

Hi.
The TV22 RF/IF deck is relatively simple, well laid out with easy access so personally I'd persevere with it. Working with it and repairing the deck is a very good learning curve and it will help your understanding of RF circuitry. With a good signal generator, a decent scope you'll be able to tie down the issues with little trouble.
The chewed core should be able to be extracted reasonably easy and I'm sure If you put a wanted on the forum someone would be able to help.
Using the TV12 deck will add in another bag of worms with fussy valves and perhaps dodgy bases.