1/2" plywood even with a backer board is not enough subfloor for tile. I would install 3/4" t&g and then 1/4" hardi board.

What size are your joists and how far do they span? How close together are they? Large format tile cannot stand any floor flex or it cracks. That's probably why the PO used the 6x6 tile. It's a lot more forgiving of floor deflection. A "sunroom" implies a structure that is already "lightly built" rather than built to normal homebuilding codes. You may need to reinforce your joists as well as installing the additional subfloor and cement board. Find out your numbers on your floor support and figure out the deflection before you go any further or you may just be giving yourself a headache of ripping out a failing floor in the future.