Is there a way to transfer app store credits to other accounts? (Having trouble with changing Apple ID account

If you switch AppleID, you won’t be able to switch back to the other AppleID for 90 days - View and remove your associated devices in iTunes - Apple Support

“When you try to associate another Apple ID with a device that was already associated, you might see a message that says, "This device is associated with another Apple ID. You cannot associate this device with another Apple ID for [number] days." Depending on when you associated your device with your Apple ID, you might need to wait up to 90 days to associate the device with another Apple ID.”

You could try purchasing Apple gift cards and sending them by email. I have never done that paying with a credit on my AppleID though, but not sure why it wouldn’t work.

See Gift Cards - Apple

My understanding of the 90 day lockout is that it is intended to stop illegal sharing of purchases amongst people not in a family sharing situation.

No, an account's balance cannot be transferred to another account, nor to buy gift cards nor to gift content.

You could create another account for use whilst you are there

Apple ID – Create

App Store & iTunes Gift Cards by Email

Switching the Apple ID shouldn't delete the installed apps. You need a credit card issued by a bank in the country the store is in, and you need a billing address in that country.