Salvaging valuable parts from a broken vintage bike
Insurers make money by promising the customer coverage and then refusing to pay up 

You do not need to accept their statements and valuations as indisputable facts.   Instead - get your own valuations and find replacements that are the same brand, spec, and age.  

Answer Don't sell that bike - its evidence.  Take this to the next level and dispute the payout, described by yourself as a pittance.   Depending on your location, that may be a Small Claims tribunal or something similar.

Don't roll over because an insurer has done their damnest to not pay you your costs.

What you do with the payout is your business, buy a new bike or old bike or repair this bike, that's your choice later.