Raise the floor with a floating floor on top of the existing floor. That looks like a nice existing floor, so probably not. That marble slab that cwhyu2 suggests would probably look pretty good.
Use shims to raise the toilet another 1/4 inch and fill the gap with caulk or plaster of Paris. There are proponents of plaster of Paris to "bed" a toilet. Either way, it would look like a 1/4 bead of caulk, I think.
Find a different toilet that will clear your extra-high closet flange as the old one did. I don't know what toilet would do that. I suspect a Unifit would work, but I am not sure.
Standard wax, no horn there.
You may be able to shim the back of the bowl, pinning the front down to the floor and make it work.
Replace the flange? That could be tough there.
The top post mentioned a marble slab under the bowl.