Home Improvement Questions? Ask a Handyman for Answers
You can't bury a junction box so a drop ceiling is your only option if you want to comply with the code. You can use a fiberglass panel (cut to fit) above the tile. You could also use a solid surface product like Swanstone but it's 1/4" thick (the fiberglass will be very thin) and it's a lot more expensive. If the top course of tile is a cap tile then the fiberglass won't stick out beyond the radius of the cap. If the top course is a regular tile then the Swanstone will be flush.
It's more difficult to install the panels with only a couple inches clearance but it can be done. But if you aren't going to bury the the boxes then sheetrock is another option.