Concrete floor finish at external doors

[tommyt]

Didn’t know if to put here or UFH forum. 

I’m having polished concrete floor and am after a flush finish to the patio over two lots of sliding doors. And also the front door. The doors are installed on compact foam. The frames will end up partially buried with 12mm protruding above FFL
 

I’m struggling to work out a neat way to add the 10mm expansion strip along the door frame.

 

If I leave it level with the frame and cut it back after I’ll see the top of it.

If I leave it shorter than FFL there will be a very thin piece of concrete above it liable to cracking. 
 

anybody have any ideas or photos of how you’ve done this before?  Can I do away with it in front of the doors?