Adobe Captivate – Passing initial score to LMS, but still allowing multiple reviews of course

This is an LMS option/setting (per SCORM). As others have stated, CP will send the score when it's completed. It's up to your LMS settings to determine how to behave on the course - take first score and set course to 'review only', then subsequent takes shouldn't save the score to the LMS...but depends on how the LMS handles it.

I'm pretty sure there's no way to force the CP project itself to determine whether the score should be passed or not based on a previous result.

I had the same question today and my LMS just stored the first value as you want. I don't know if the company that manages LMS changed that, but at the Captivate I kept the "Infinite tries option" and LMS just received the first score.

If you have set Captivate to allow more than one attempt on the quiz, the user's score won't usually be sent to the LMS until the user terminates the session by progressing beyond the Quiz Results slide.  This means that even though the user may have made a FEW attempts on the quiz WITHIN a single Captivate session, only ONE attempt may actually be registered as a score with the LMS, and the LMS may then regard this as ONE attempt (because the user only launched the course module ONCE and only ONE score was received.

If you wanted the LMS to see each and every attempt the learner made on the quiz inside the Captivate module, you would need to set the Captivate Quiz > Pass or Fail settings to only allow ONE attempt, which would then mean the learner had to close down the module and relaunch it from the LMS to make another attempt.

Whether or not your LMS gives you the option to only keep the first score it receives, or the highest score, or the average of all attempts, will depend on your specific LMS.  You need to check what the options are in the LMS documentation.  They all differ.