Im going to throw my two cents in on a design standpoint...
For the sake of symmetry, size cabinetry to match wall lengths. What's on the right ride? There is no wall/window/architectural detail in your first photo closing the space to the right of the fireplace..? if the gaps between the end of the built in and start of whatever ends on the right are the same on both sides it will give you the appearance of symmetry, so instead of doing 36" on either side, do 36" on one side and a 39" on the other- I know its not exact, but generally pre-made cabinets come in 3" increments. I assume you would do two on each side? It will be close enough. Most people's eyes cant tell the difference between a 36" and 39" cabinet or a 3" or 4" space. Its relative to the length of the discrepancy and the length of the space it occupies- under 10% is a good rule.
The overlap of your facing (1x or molding, or use 1x and route decorative edge) is only relevant on the bottom. Overlaps on the sides (up to 1") and top (as much as you'd like, I have 3" on my built ins to hide down lights) are beneficial, but you do NOT want your face frame to create a lip at the bottom- this always looks bad. The top of the base trim should be at or below the top of the lowest shelf.
If you intend to bring the two outside ends of your built in to the outside edge of your space (ie walls on both sides) and crown the whole room, you have to bring the built ins to the ceiling.
If it were me- and I am a crown moulding lunatic- I use that S&%T like hot sauce- I put it on everything.. I would leave the rest of the room bare, and do a really big built up two or three piece crown only on the built ins and space it about 3" down from the ceiling at its highest point- it will throw really nice shadows, but for this to work, you'd have to do a three piece built in, one on either side of the fireplace and one in the center- where the center piece would be at least as far forward as the side panels and it doesn't look like your plan goes that way. If it will dive back in toward the wall over the fireplace you have to crown the whole space to the ceiling for it to look right. I know you have a wall on the left side of the fireplace, but what's on the right side? Is there a wall there, or does it run into another space, like a dining nook or something?
My only concern is with depth- your fireplace looks like it sits almost flush to the wall... how deep will these purchased cabinets be? I am afraid they will make the fireplace look cheesey... like its stuck on.. it may detract from the architectural element of the fireplace itself, so maybe a wider mantle with a built up edge/frame on the left and right side is in order... a recessed fireplace would look fine if you have some sort of trim work frame to bring it out to the built in. You'll need to address that width difference. I think having the 3/4" wide cabinet edge sticking out from the wall is insufficient for that transition. For the sake of cohesive design you'll need some sort of decorative spacer to address it.
I cant wait to see the finished product.