I would like to change my Apple Music payment to a different date. How can I do that?

You cannot change the billing date.

you can cancel the plan temporarily until the correct billing date when you re subscribe it is inconvenient but the only way to change the date

I don’t think so. Too many posts on here saying they couldn’t get it back after renewing,

Some of the terms have changed.

Cancelling Apple Music will remove all their Apple music that they most likely won’t get back.

https://www.apple.com/legal/internet-services/itunes/ca/terms.html

”.  When your Apple Music membership ends, you will lose access to any feature of Apple Music that requires a membership, including but not limited to access to Apple Music songs stored on your device, and iCloud Music Library. ......”

They lose access to the music and features however when they renew the subscription they should regain access to the content