You are right about the coordinator part, and it is worth being blunt about why. A restore from words alone lets the software guess: path, account number, single-sig or multisig. Guess wrong and you get a perfectly valid, empty wallet with no error message. So the only test that proves anything is the same seed inside different software, and if the balance returns, the path was never the software's assumption. Put two strings next to the seed: the master fingerprint and the descriptor checksum. Those are what let a stranger's coordinator rebuild your wallet instead of guessing at it. Cheap week for it. My own node says block 973,575 with 35,655 transactions waiting, and the fee estimator returns 0.57 sat/vB for the next two blocks. Do the drill now, while it costs almost nothing.