I second the Leer recommendation. I am very happy with my HF650m and it meets all of the criteria you listed.
Another member posted a thorough review here https://www.f150gen14.com/forum/threads/leer-hf650m-tonneau-cover-review-with-photos-install-first-impressions.6966/
I pulled my tails apart to confirm sizes (302A BLIS) and as you said the reverse light is LED and it seems to be a self contained module not easily replaced. As such I'll be doing some sort of bumper mounted pod solution for more reverse light coverage.
I ordered the brake/turn bulbs from DD...
Thanks for this post. Any reason to go with 3157 bulbs from Amazon or elsewhere vs going with DD, aside from cost?
Also, did you do the white reverse lights or just the 4 red lights? I'm getting conflicting information if those are 3157 as well or 7443