[MiniMe]

Here is the design that I have in mind
It will sit over a 3/4" subfloor edge on each side, flush with the floor
The North and South of the picture ends have been represented that way to give a clear picture of the cuts required but they will be 3/4" wide co properly visually balance the look of the register

I do not know how to safely route the long pieces, for the shorter ones I am building a jig

 

[MiniMe]

Thank you Tom
I just realized that for the long pieces it could be much easier cut them with the table saw
I was thinking about a way to do it on the router table not with the plunge router