2008 Mazda 3 P0753 Fault: Solenoid A Issue, Jerking in Gear Shifts, TCM Replacement Cost Concern

While driving, I experienced a sudden loud bang, which I believe was caused by an incorrect gear shift. Immediately after, the check engine light turned on, and the diagnostic code P0753 (Bad Solenoid A) appeared. The car drove normally until I got home, but it now jerks noticeably when shifting between drive and reverse. I attempted a DIY repair by flushing the transmission fluid and replacing the solenoid. When tested, the new solenoid produced a clicking sound, leading me to suspect it was faulty — however, after reassembly, the issue persisted. I then checked the electrical connections, which were found to be intact and properly connected. The problem remains unresolved. Given that the transmission fluid and wiring are not at fault, I'm now considering whether the issue lies with the Transmission Control Module (TCM). Before spending $500 on a new TCM, I'd like to confirm if there's another possible cause or diagnostic step I should take. Any insights from owners of 2008 Mazda 3 models would be greatly appreciated.