Keeping "run-off" out is definitely one function of the coamings. To that end, they are installed with a foam strip (I used some closed cell foam tape for outdoor or marine use). Otherwise the water will just drip behind them.
However, I've occasionally manged to "bury the rail" briefly, and in that situation, the coamings do extend the angle of heel just a bit. Really can't say whether the water was highest near the front or the rear of the cockpit. In flat water, the height of the water around the boat is determined by the stern wave. At speeds close to hull speed, the first crest of the stern wave is a short distance before the transom, further forward if you are sailing slower. The trough would be around the middle of the boat. (Once you add wind waves, this picture isn't quite as simple any more).
So, not only is the freeboard lowest, the water is the highest at some point at the rear of the boat. Interesting. However, it seems to not present problems in practice. (And whether a straight-line shape will look acceptable that's really up to you
).
As for the traveller, the difference is that it allows you to maintain sail shape while spilling wind. (Same effect as you would with a high purchase vang used up-wind). With a mainsheet only, the minute you reduce tension the boom not only goes out, but it does go up a bit, opening the leech. So, yes, that gives you more control.
As for the BBQ plate, how heavy is it? The standard CB is 25 lbs (before subtracting any loss due to the immersion). Any additional weight you add that low will definitely add to the stability - but mainly when the boat is heeled substantially. The weight has to be off the centerline before it can develop a righting moment. Its not unusual for keelboats to be sailed with the rail buried (about 30 degrees) which means the center of gravity moves off-centerline by about half of its depth below the center of buoyancy. And, as you can see from the diagram, the center of buoyancy itself shifts outboard in the other direction because of asymmetric immersion.
At smaller angles of heel, shifting the "live ballast" has much greater effect, because the lever arm is longer and you can directly increase the distance from the center of buoyancy and therefore increase the lever arm further.
However, when it comes to recover from a capsize, I could see solid advantages to a bit of extra weight down there. The lever arm would be optimal at those angles and might be enough to prevent, or at least slow down any tendency to turtle.
We are all curious to hear how she sails with that modification.