You don't have the new MacBook yet, is this correct?
What you could try:
When the new MBP comes, put it on the table but DO NOT OPEN THE LID YET.
Connect your tm backup.
NOW open the lid.
Begin setup.
DO NOT create a new account.
When setup assistant asks if you wish to migrate from another drive, YES, you do, so "point the way" to the tm backup.
SA will take a while to "digest" the backup, then present you with a list of stuff to migrate.
You want to migrate ONLY your previous account, so you must UNCHECK everything else.
MORE...
I believe with ONLY your account checked, you have the option to "go into" the account and check/uncheck things like music, pictures, etc.
Disclaimer: never did this myself, you'll have to try to find out.
So... you would want to UNCHECK everything EXCEPT "Music" in your account.
Then, let SA do its thing, and it should migrate ONLY
- your account (basically empty)
and
- your music folder (from the old account).
There are other ways, but it will be up to others to point them out.