Your bottom line issue is removing Find My when the phone is incapable of entering the password. The standard procedure would be to get the phone repaired so you can now do things the way they are designed to be done. However, you're in a bit of a Catch 22 situation here. You probably don't want to pay for a repair of something you are going to trade in, but then Apple likely won't accept it if you don't remove the lock. The one thing I can think of is to have the lock removed from Apple's database remotely:
Apple can completely reset a device if a person can provide sufficient evidence of valid ownership. Do this online at: Activation Lock support request - https://al-support.apple.com/#/additional-support Apple says, "Proof of ownership documentation is required," but does not detail what currently constitutes proof. Prior to this new online service Apple typically required the original receipt issued by Apple or an Apple Authorized Reseller and documented provenance (so typically it would be the original owner who does this, or a descendant with legal proof of ownership). This will give you access to the device but won't restore access to the account used to lock it. There is nothing that can be done to expedite an Activation Lock request.
Apple recommends you "Keep your receipt after you buy an Apple device" --> Keep your receipt after you buy an Apple device - Apple Support
