I agree. The TK agents would have no clue about upgrading with UA miles. Big mistake inquiring and relying on info from TK agents of this nature. Most likely the agent thought the OP wanted to upgrade with TK M&S miles.

The only option is to hope that availability will appear shortly/days before departure; or travel as booked.

If there is a schedule change of more than 15min or cancellation the OP can is able cancel and get a full refund (if booked directly with TK).