As such, if ECDSA is suddenly completely broken such that there isn't time to move to a new signature algorithm, then an industry of trusted mining will have to evolve. It will become necessary to be able to submit a transaction directly to a trusted miner that will confirm the transaction into a block without relaying it to others that might modify before it is confirmed.
The block still could become orphaned, even trusted miners don't guarantee that ur coins r 100% safe.
Correct. It would take a significant effort and solving some serious trust issues to spend bitcoins into a transaction that uses a new signature algorithm of ECDSA were to be suddenly completely broken.
Fortunately:
Far more likely is that these algorithms slowly become slightly weaker over time. As such there is plenty of time to replace any of them before they become a serious problem.