I personally see it as counter productive that someone "claims" the rescue. It's in my opinion better that a mission seems as available as the next.
However, we have added the following in the description which is pretty much the same thing as your paragraph 1, but less visible.
If you plan to visit a geocache to look for a trackable, we suggest that you write a note in the rescue missions log book to show others of your intent. Once you have checked the geocache, log either a DNF or a Found to show your results.
Markers which seem claimed would get much lesser clicks, which as I see it is just a downside.
But keep the discussion going, we are looking for input, maybe we are wrong. I believe it also will be easier to decide when the system has been running for a while and one can see how it's used.
PS! The numbers on the markers have been changed from the age in days of the mission, to number of logs on the mission.