request for help - transfering money between banks cheaply

Does anyone have recommendations on how to transfer money between bank accounts held at two diferent institutions cheaply?

I have to move money into an out of state bank. I can mail it, but it will take about a week to process - I don't have that much time.

Neither the destination bank nor my bank know how to do a one time EFT / ACH transaction - does anyone have a bank that can?

It looks like I'm left with either overnnighting a check OR wire transfer.

Wire transfer is guaranteed to get there. It costs $12 to receive and $14 to send. For a total of $26.

Overnight mail would cost about $18, but is not guaranteed to be processed over night.

What would you do?

I need the money credited to the account by Wed.

Thanks and have a good weekend.

Makingourway