"Perimeter puzzles" rely on a revealer to makes sense of the answers around the edges. SUBMERGED didn't make sense to me at first — shouldn't that mean two "sub" answers will merge, i.e. cross? But upon further thought, SUBMERGED instructs the solver to "merge SUB with what's in the entry." Interesting concept!
Ruth did a good job selecting theme answers, choosing ones that looked perfectly normal in the grid — not to mention, ones that intersect so nicely in the four corners! I stared at the very first square for the longest time, wonder how LIME could make sense for [Lofty in thought or manner]. I do like limes, but are they really lofty? Finally figuring that out was lime. Er, (sub)LIME.
I had a head-scratching moment upon uncovering (sub)URBAN and (sub)TRACT, as those didn't "merge" with another theme answer. And then I kicked myself, remembering that SUBMERGED just meant "add SUB." Dang it!
Ruth is absolutely right, perimeter puzzles are notoriously difficult to fill well, given the constraint of having two crossing "themers" in the corners (I swore them off after my last one). I was very pleased with Ruth's execution in the lower right — SASHIMI along with not a drop of crossword glue? Beautiful work, especially given the degree of difficulty.
The lower left is more typical in terms of the liabilities seen in perimeter puzzles. ALIENEE is a valid word, but I don't know how many (non-lawyer) solvers will clap at this one. Along with IN ME and (the very minor) EST, it's got a few flaws.
Perimeter puzzles are also notorious for making it difficult to work in great long fill. With all the constraints already placed on the grid, it's so tough to take advantage of those long slots. TEA HOUSE is quite nice, but PANELIST to me is more neutral, as are BETAMAX, SLEEVES, ESSENES, etc.
I like when struggle suddenly flips to a moment of discovery, so I liked the concept. There were a few more dabs of crossword glue than I like, but that's part of the nature of this theme style.