Wait. Using the same seed means the private keys are on the new ledger. But under all new public keys?
The goal is to send the coins from ledger A to ledger B, without being able to trace them.
You can't
send coins from ledger A to B without a public transaction record. You either move the seed to another ledger or you move the coins directly through a transaction. Mix the coins or CoinJoin them and then send them to ledger B. This way, your trace is lost.
There is literally no other way to move coins. You either use the same seed or you move them to another address.