Someone can correct this if I’m off-base, but…
I’d open NEW SM account with your new email, then ask DL to merge your old, dormant account with the new one. It *feels* more like going in through a side entrance rather than possibly trying a method rife with potential security issues.
Obviously, they’ll ask for the creds on your old account, but that’s the very reason you opened the new account, under the same name, etc.
I’ve done this with a couple other companies who refuse to deal with unrecoverable credentials. Never DL though, so it may be a bust.