Wait. Using the same seed means the private keys are on the new ledger. But under all new public keys?
You will have same private keys, same public keys and same addresses in the new ledger.
By importing the seed into the new ledger, you will have access to the fund you had in the old device.
Perhaps I was not clear. The goal is to get the coins from point A to Point B without a trace. Do I have to spell it out any more clearly?? Lol.