There are a few factors that you need to consider here.

First concern: According to the photo (plan), the intended flat ceiling at the 12' height is a space with the dimensions of 12' (W) x 18' (L) with a 12' high ceiling, this is going to come off as a long rectangular silo. The ceiling than starts a downward slope to the back wall.... the break bisects your fireplace, so half of your fire place is visually going to be in the 12' ceiling space and the other half is going to be on the sloped ceiling side...........in my mind this is going to make for a funky look transition wise and quite possibly a visual faux pas when it comes to anything on the wall here (painting, mirror, large screen TV)..........it's going to look awkward and not really relating to anything on the floor plans.....Is this fireplace at floor level ( it looks like somebody has sketched in a code required non-combustible hearth in front of it ) or is this a raised fire pit with raised hearth.......what is the finishing above the fire opening, does it go up to the ceiling.........which would tend to lead one's eye directly at the point of "ut oh, what's going on there"

Second concern: What is the elevation where the sloped wall meets the back wall? Is it coming back to the 9' bearing wall height of the back wall or is it higher? Either way, you'll have another funky end wall visual effect at the Kitchen end of your Great Room.

To be honest it's going to result in anything but a "seamless transition"......not to mention the angled cabinet peninsula that is going to jut out into the space resulting in some awkward lighting effects at the sink station......where's the lighting going there, you got the ceiling break falling half over the sink.....to get an even lightening effect on this surface you're going to be limited to an aim-able track light........

Throw in the arched openings to the Dining Room and Foyer and you've got a lot going on here with the ceiling and the transitions...............I'm wondering did the builder design this for you or somebody else? There seems to be a lot of changes (visually) with the ceiling and the openings that, in my opinion is going to drastically detract from the tray ceiling in the Dining Room.

If I was the designer, I would have suggested a raised flat ceiling in the Foyer with no header at the transition to the Great Room that flowed into the Great Room...........both of these spaces would be at the same height as the raised portion of Dining Room ceiling and the lower portion of the tray at the same height as the Kitchen Ceiling...........it would certainly help with the lighting possibilities and get rid of those awkward transitions.

I would strongly suggest a 3D study model be constructed in Sketchup (free Google Modeling application) of this area ( Foyer, Great Room, Dining Room and Kitchen) to study the spatial feel.

Another solution I would consider would be a tray ceiling in the Great Room, with the raised portion a 10' ( or same elevation as the tray in the DR ) and the lower portion at the same elevation as the Kitchen Dining Room and the Foyer with no bulkheads a the openings. This too would clean up the ceiling while yet visually making the DR and GR a distinctive space and improve the lighting possibilities.

Just my observations..........and with that and my $1.79, I can get a large coffee to go at Mapco this morning on my way to a remodeling project I'm helping a client with.