Did you send melon tokens to the bittrex deposit address for Ethereum? if yes then it's your fault and i doubt bittrex will care to dig out their private keys, and send back the melon manually to you. It's just very unlikely that they will do so with the sheer amount of complaints i've read about them.
Exchanges like bitfinex have clear warnings and procedures about sending the wrong token to the wrong address, i'm sure bittrex does too.
THeir support is extremely slow at the moment so 60 days without a response is only natural.
Also, please move this to exchanges in service discussions since i don't see any scams here.