Your Ceiling treatment has dealt with enough of the reflection off the ceiling to get you by, but the Wall to the left needs about 4' of masking.
As for painting the Screen with the trim on, I think you must be resigned to avoiding such. Even if the Black material was removed, still the raised edge of the 1x would prevent edging in the paint enough to create problems.
AIVA makes a Calibration Disc you can get at Local A/V Stores (...and the Web...) , as does Video Essentials. Both are going to be quite less expensive than any of the tools mentioned/used in the Calibration Forums.
The real trouble is that the BOC only has so much to offer / deal with, and you cannot magically tweak the HD20 into higher contrast levels without affecting other elements of the image too much. Lower brightness and increase the Contrast setting too much respectfully and you'll destroy both the dynamics of the image and erase much detail. A Calibration can / will help, but miracles are not to be expected.
Really...and it pains me greatly to say such....your gonna have to do a Roll on a Neutral Gray 8.0. It's the only option open to you to really affect your performance envelope. After carefully masking the inside raised edge of the Black Border with Blue Tape, by going around the edges with a 2" Foam Trim Roller (...with a "light load" of paint...) 2x while being careful to feather out the inside (screen-ward) edge, and then carefully rolling into that area with a 6" Hard foam Finish roller, that is about the only method you can use to get a decent lay of paint close enough to the inside edges so as not to leave a noticeable "ring" around the inside.
Using a "Flat Sheened" Gray is most advisable as when it dries it will tend to blend well with any / all the other previous "feathered" paint lines.
With judicious masking of that Wall, and by going with a Flat NGray, your overall contrast off-screen will then take a dramatic turn for the better. Calibration should still be done, but trying to get deeper blacks via attenuating both Color intensity and light output will not be on the agenda.
I wish you good luck with the painting. Just take the edging process slow and carefully...as far as not applying too thickly with the 2" roller, but do not tarry on rolling using the 6" finish roller into the area. Just as soon as the 2x coating of paint around the edges has dried to the touch, roll into it with your first full screen coating.
As I see it, you made a decision to keep your Screen construction simple, and that worked well, but you put too much faith in the raw BOC's ability to deliver a decent image. Leastwise with a PJ with under 5K Dynamic Contrast. You absolutely must use the HD20's brightness and a Gray surface to mitigate the weaker Contrast output. No "Ifs", "&s" or "Buts" about it.
Go get'ter dun.