Clearances to combustibles for masonry fireplaces are found in the building code. Clearances for manufactured metal inserts or free standing stoves will be found in the manufacturer's installation instructions.

The clearances you mention are much larger than required for traditional masonry fireplaces.

I thought it was the other way around. Rather than the clearances being much larger for the inserts, I thought the clearance requirements were much larger for the old style masonry fireplaces.

We are also remodeling and want a low height. There are numerous inserts (in our case, we are installing a gas insert but still a metal insert) that are in the range of 24 or 25 inches high. If we place these at floor level which is what we plan to do since the floor of the existing firebox is same level as the floor of the room, then I'm hoping that we can add at most 8 inches of tile above the insert which puts the top of the fireplace at 33 inches.
We are not going to use a mantle but instead use a fireplace canopy or fireplace hood (3 to 6 inch type of strip of metal) which I hope we can install at the seam of the insert where it meets the tile surround.
This means the TV we plan to install over this fireplace will have its bottom length possibly as low as 33 inches above the floor.
We have a fireplace guy coming on Wednesday (5 days from now) and should know more then.
I do know that if we were going to leave the fireplace as it was as a wood burning fireplace (without an insert), we would need at least 12 inches of tile above the firebox top edge before installing a mantle (or in our case now, a TV).
Crossing my fingers...