Turkish Airlines cancelled my IST-AMM flight, what are my options?

I booked on a flight from Houston (IAH) to Amman (AMM) via Istanbul (IST). Turkish airlines cancelled the IST-AMM leg. And gave me the option to change the flight free of additional fees. I found alternative Royal Jordanian (RJ) flight CODESHARED by Turkish Airlines and when I chose on website, application, other devices all errored and glitched multiple times. Called the hotline and they claimed my ticket isn’t Codeshare and therefore cannot complete the change and I should either submit a feedback form or get my refund. For context, my flight was supposed to be in 7days. I called again and this time different agent proposed to me to fly either to Lebanon or Aqaba in jordan —Different city than Amman— but I found it absurd and called again. This time a nice agent chose for me the Royal Jordanian segment of IST-AMM I desired and told me he reserved it but the ticketing process is pending review. He told me the team will call me to take my final permission in the approval. Unfortunately, the next day, the Royal Jordanian flight disappeared and is replaced by duplication of the 2 segments IAH-IST, IST-AMM totaling 4 legs on the website and making the ticket invalid. I called their hotline again, an agent tried to create from scratch the ticket because he thought the ticketing process originally got cancelled because of not available seats. In the end he also told me since my ticket is not Codeshare the change in any operator other than Turkish Airlines isn’t feasible and that the nearest Turkish Airline flight is by 30th April. And that the rerouting to Aqaba or Lebanon isn’t feasible. I tried to tell him how this is not voluntary rerouting and I need to complete the destination I booked especially when the solution is clear for Royal Jordanian flight. He agreed but disagreed that he can do anything about it. So I demanded to escalate and he wrote a note. I closed the call and wrote a request on feedback form. Next day, still nothing, I contacted the hotline and escalated the issue further.

Other than cancelling the ticket. What choices do I have left? This is frustrating me.