Your front door isn't going to open and you surely will have a problem with any entry rug, not to mention your base skirting will require major work and transition to adjacent areas!! . Either take the under flooring down, or investigate a different tile frankly. Perhaps a porcelain. Worth the restocking fee for all the trouble.

Particle board isn't suitable as a subfloor for tile ever. EVER. It must come up, and be replaced with 3/4 plywood. At that time, you need to do the math to assess whether or not the joists actually provide enough support to do tile without cracking. Large format natural stone needs a subfloor over twice as stiff as for wood flooring. If they need support, which is highly likely, then when the subfloor is open is the time to install it. Then, to minimize the height build up, you can do an uncoupling membrane like Ditra.

You need an expert GC on this job who employs an expert tile mechanic. This isn't a simple job. No job that needs potential structural issues addressed is simple.

Listen to the above declaration!

Jenarm, What did you end up doing, and what problems did you have,? Did it turn out OK?