Folks, first of all, thank you all again for your advice.

My final update on how our situation resolved Turkish Airlines Booking Issue (with you all's help to level-set expectations):

Booking Resolution:
1. Worked with Oojo (booking agency) to find an alternative flight.
2. New flight: Single connection, long layover in Istanbul, about a week later than original.
3. Accepted this option, grateful for a return flight during peak summer albeit having to change a lot of plans, no other option seemed effective for us in the end.

Key Issues Resolved:
1. AnadoluJet concern: Not an issue in final booking.
2. Business Class upgrade: Not pursued/offered in final resolution.
3. Chargeback: Didn't pursue this option.
4. Twitter support: Remained ineffective throughout the process.

Challenges Faced:
1. Communication issues between Turkish Airlines and Oojo.
2. Inability to get clear refund information.
3. Difficulty in requesting partial refund calculation before rebooking.

Learnings:
1. Turns out the flight schedule changes are due to the recent regional conflicts.
2. In times of conflict, booking directly with airlines may be better than using travel agencies, even if a bit more expensive. Oojo didn't offer the two-stop option, which by the end of this, seemed like a better option due to the week delay in getting back.
3. Forum advice helped set realistic expectations and dispel assumptions about ticket class upgrades.

Corrections:
1. Austrian flight pricing: My mistake - prices were per passenger, not total.

Final Thoughts:
While the outcome wasn't ideal, your advice helped us reach a resolution faster and with better understanding. We're grateful for the community's expertise in helping navigate this situation. Thank you all.