The plumbers don't use a lo-heel outlet in that position. That's meant to be used in the vertical.
You can use a wye fitting after the 90 bend on the toilet and pick up the lav that way.
It would be closet flange, 90 bend, wye fitting and then toward the santee on your cast iron stack.
We don't really pay much attention to what we find. We try to do things an inspector would pass on an inspection with permits.
The Carlyle will need 9-1/4" from the finished wall to center with the 10" Unifit.
Floor mold will fit at the wall.