And by saying "company that recycles wallets", you mean any password-recovery services?
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I assume that, yes. Otherwise the second sentence would make little sense in this context!
Sending hashes is a very good idea, the only question is whether the recovery service would accept it. Classically, they collect a fee on the coins in the wallet, for example 20%:
Source
@OP
The bottom line is that you actually have nothing to lose and in the best case you get access to your coins again. If you turn to a service that has a good reputation, then your situation can at least not get any worse.