Again, from the newbie here (but I have read a lot of what everyone else has written, and I LOVE this site and the forums!), I have to agree totally with the Brendan Fraser suggestion. Just re-watch "Blast from the Past" to see his comedic talents, the Mummy series highlights his "action" capabilities (and humor too -- "I HATE mummies!"), and he has the looks. Also adding a moustache on his face would be a totally different look for him so it would tend to make him less recognizable as Brendan and perhaps more acceptable to us diehard Selleck fans as a substitute for Selleck.
For a Rick character, I would really like a guy who can actually ACT. Larry Manetti may be a great guy, but IMO, he canNOT act and never could. He always sounded to me as though he were reading lines off a cue-card AND over-acting (remember the jerk reaction in the shovel scene in the opening credits? That ALWAYS looks over-acting to me -- again, JMO!). Perhaps Rick could be made more appeal-able by a better actor. I think Matthew Perry could do this. He can pull off comedy ("Friends," of course) and "The Whole Nine/Ten Yards" series, plus straight drama in "The Ron Clark Story."
For TC, how about the black doctor from "Scrubs"? (I'm sorry I don't remember his name right now). He can be strong, capable, but could probably pull off the frustration, with humor, with Magnum's shenanigans. Though I wouldn't object to Eddie Murphy, but would he be gracious enough to play second fiddle?
The sticking point for casting, other than TSM, of course, is the critical Higgins character. Though he wouldn't fit the "body type" of the original JQH, I think Alan Rickman (who has a history with TS in "QDU") could pull off the British persnickety-ness and condescension to TSM, yet be there to pull through when needed.
And, of course, let's get the now-senior citizen Julie Andrews to do a parody of Agatha. That could be the only parody-type role, and I think JA would chew the scenery doing that. And it would make her attraction to Higgins a little more believable (and hopeful) for her to play opposite Alan Rickman. So they could finally get together at the end, and we could enjoy it, because we really didn't want Hillerman to have to settle for Chumley (though she was good in the role, we [at least I] just wanted better for JQH), but Rickman and Andrews would make a good "together at the end" resolution for that character.
This would be casting younger (than the current cast) in a new movie in present-day time.
However, if we go to using the older characters in a new movie (a la "where are they now?"), I liked the idea that Walt suggested (if we use the original, older cast) about Magnum's daughter being Naval Intelligence and TSM has to gather the "old gang" and go perform a rescue. Could Lucy Lui be the grown daughter, as wasn't Michelle's daugher Amerasian (though if that were the case, we'd really need someone who looks more like Nancy Kwan, but I don't know of a current actress who looks Caucasian with only a slight Oriental influence the way Nancy Kwan did)? But was she supposed to be TSM's daughter, not the General's? The child who played the part did not look like a cross of Thomas and Michelle to me.
I think it wouldn't HAVE to be an "action" story, if written correctly, like maybe a serial killer/kidnapper took the daughter and it takes cunning and substitute suspense for action by the entire crew -- a la Morgan Freeman as Dr. Alex Cross -- to find and rescue the daughter, while she's doing her own efforts (a la Ashley Judd in "Kiss the Girls" and the female FBI agent in "Along Came a Spider") to thwart the kidnapper/killer.
Just throwing out ideas here. As though anyone actually making the movie would actually pay any attention to any suggestions from the general lay public . . . .