I haven't tested this in a Ti Tri, but I've just done a few test boils with a Fosters can, an unmodified Starlyte stove paired with Zelphs Titan-3 windscreen, and a slightly shorter MYOG screen in a similar style.
Using a Ti floor, boil times decreased by between 30 seconds and a minute and fuel efficiency actually improved (very slightly). Using a foil floor knocked another approximately 30 seconds off the boil time, but was slightly less efficient. I guess the Ti floor hit a sweet spot where it was reflecting enough heat to improve the boil time, but not enough to overheat the stove and decrease efficiency.
I doubt you generalise these results to different stoves and set-ups, though.
BTW, the Starlyte and Titan-3 seems to be an incredibly efficient set up for the Fosters can, at least at low altitude. I'd still love to hear from anybody with experience at high altitude.