Tiling over 1/2in subfloor with 1/2in Hardiebacker
Sounds like you got it under control, but what you might consider instead of 5/8 inch plywood is 1/2 inch plywood (so now the floor is 1/2 inch higher). This is plenty thick for a finish tile floor. It would be wise however to install the new plywood sub-floor perpendicular to the plywood floor it will cover. Also consider fastening it with screws and or ring shank or spiral nails. Bridging between floor joists was the way to go for added support under the floor. Give a final check by walking the floor listening for squeaks and looking for any deflection (bounce). To accommodate the 1/2 inch difference in floor heights, purchase or cut a transition strip of hard wood.