Ive been working on preparing a small bathroom for a tile install. The subfloor is plywood over I-beam type joists. There is a finished basement below. The joists are 16 on center and assuming they span about the width of the house they are 16ft. Generally the floor seems fairly stiff except around a floor register (3x12) right where anyone will walk entering the bathroom. I can push down on the plywood near the register and see the floor deflect (1/16"?). What should I do? I hate to add a layer of plywood as this will put the final height of the tile way above (5/8"+new layer) the carpeted hallway.

Options Im kicking around:
1. Suck it up and add a layer of whatever is the stiffest best subfloor based on your recommendations.
2. Go in the basement and remove the drywall ceiling in the area below the plywood that is deflecting and try to back it up.
3. Totally remove all (or part) of the plywood in the 60x84 floor area of the bathroom and install whatever is the best (low profile) subfloor?

Im not under any real time constraint, and want to do whatever is best; I do have a table saw etc. but limited expertise. Any advice would be appreciated.
Thanks, Wayne