The gap is the result of improper alignment when assembled, and your dealer's body shop should be able to correct this. The cedar shingle strick won't work for this type.
Now, on to a repair for the bumper popping that's permanent and doesn't involve wood. Get a roll of 3M automotive trim tape. Get a long, thin flat blade screw driver or some implement because you'll be inserting the tape. Get a piece of corrugated cardboard about 5 inches long by 3 inches wide.
The spot where the bumper cover keeps popping off from heat warping is your target area. Cut a 1.5 inch by 0.5 inch piece of the 3M tape. Gently pry the bumper cover away and place the 3M tape on the black bracket where the bumper cover's snap is headed to lock in.
Once the tape is in place and the bumper cover is still popped, kneeling in front of the bumper push the bumper cover up with one hand while gently pressing the tab back in place. If you're careful it will slide right over the 3M tape. Once you hear the pop as it snaps in, press down firmly along the mounting tab where the tape/tab is. Granted, this is typically where the headlight/bumper cover/grille meet, but you can do it. Hold it for a couple of minutes.
Now, fold the corrugated in half so it forms a cardboard wedge. Push it between the headlight assembly and the tab/tape you just snapped in. Leave it for 12 to 24 hours. The longer, the better.
After the time has elapsed, remove the cardboard. The tab has adhered to the bracket and is being held in place by the 3M tape and the tab itself. The 3M tape is a super strong, acrylic adhesive. I used it to stick up a piece of split siding 12 years ago, and it's still going strong.
This will fix the issue. No new bracket. No dealer idiots playing around. No new bumper with dealer paint not maching your factory finish.