I'm a longtime Parker/Spenser fan, and I've been open to the idea of continuing Spenser for a year now. To me, Spenser casts too long a shadow on contemporary P.I. fiction to die with Parker.
...[W]ith TV's Spenser: For Hire, Parker was credited as "Creative Consultant" but claimed that simply meant he cashed a check every week. TV made some changes to the characters that didn't sit well with me, but the show did well enough on its own to run for three seasons (1985-88).
As you point out, the Jesse Stone movies also have a continuity independent of the books. I think that was a good decision, given that Tom Selleck is much older than the Stone of the books, and if the movies followed the books to the letter, they would hold no surprise for faithful readers.
I can't muster much interest in Brandman's Stone novels, and what I've read of Killing The Blues hasn't helped. However, Atkins' track record as an author is much better than Brandman's, and Ace's novel The Ranger [newly nominated for the MWA's Best Novel Edgar® Award -ed.] convinces me he can write in the Parker vein.