Changing crystals most likely wont help you.
Typically Futaba and Hitec Tx/Rx will play nice because theyre whats termed negative shift.
JR and Airtronics will usually play nice together because theyre positive shift.

Some Airtronics Rx's and others are capable of both negative and positive shift.
Unfortunately thou it sounds like your Airtronics Rx isnt compatible with your Futaba Tx.

If you give us the model of your Rx that would help.

Cheers.