I used Suzuki fluid because, luckily for me, I can get it at a decent ex-dealer/service center and at a good price. There are several other threads on this forum such as this one where others have found different branded CVT fluid that is marked as Suzuki Green/Shell compatible.
You don't know it's not the TCM...however, the fluid change is the easiest and relatively least costly DIY remedy. As I said, I feel replacing that cooler return filter is a must After that, you will need to find a service center that can diag the TCM/trans based upon the TSB.
As far as disconnecting the battery, they want that done mainly for safety. I don't unless I'm working on something electrical. Just don't go laying tools on the battery where it can sort to chassis gnd. By disconnecting battery for a length of time, you've seen operational data lost from memory, a hard reset so to speak. It will reset as you drive over time.
2010 Kizashi GTS, CVT, iAWD (3/10 build date)
2011 SX4 Premium Hatch, CVT, iAWD (12/10 build date)
2018 Mazda CX-5 iAWD Touring
2014 Wrangler JKUW (GONE, traded
1991 Samurai, 5-Speed, EFI, Soft-Top (