You pretty much lost me in the first line of your post:
"I have seen a couple of threads / posts and even articles claiming that the PS3 made one of the greatest comebacks and is a profitable business for Sony. I just had to clear this up."
I've seen a couple of threads discussing a PS3 turnaround, but the focus to me seemed to always be on how they turned a disasterous launch which could well have destroyed the brand of the previous generation's leading console into the top-selling home console for the last two years and a viable product in the market.
Perhaps there have been some other threads discussing the financial side that I've missed.
Regarding that, I definitely agree that Sony made losses with the PS3 that they'll never recover, but I also think we'll never know the true extent of it. Losses made during the early years were hidden in profits being made from PS2 & PSP sales; while profits made in recent years will have been eaten by Vita losses and R&D and lately PS4 R&D (and probably losses, too). Plus, I suspect there's probably a fair few more years of PS3 sales to come.
You've still made a well-educated and interesting OP, but yeah, with so much "let's be conservative" and "an educated guess" in there, it really is impossible to tell.