I haven't seen any stock Rogers FTFs around but you should be able to flash others. My Xperia T LT30a is a Bell unit and I have flashed a bunch of different FTF's (mostly LT30p ones). Since your phone is in bad shape right now, I think you should just flash one to see if it helps. If you want an older Bell FTF, I am currently uploading it to multiupload (will edit and post link after it is finished). It is a stock Bell FTF: LT30a_9.1.A.0.489_Xperia TL (Bell)
. And finally it uploaded: http://www.multiupload.nl/1BS5AUH6TF
If you're curious about the others (LT30p) FTF's but are hesitant, I can tell you that I have flashed these on my phone using Flashtool without problems:
If you're having trouble finding them or links are dead, and you want one of those let me know and I will upload. Good luck!