How to cultivate relationships/recommendors as an introvert
This question seems to be incorrectly premised; this is particularly evident in the following sentence:


  I'm realizing that one of the things I'm missing is a strong recommendation from a senior academic that isn't on my committee or a professor I've taken courses from.


Why do you feel that is missing? A good reference is one that assesses your suitability for the post you're applying for. As such, it will need to be written by someone with knowledge of (most of) the following:


Candidate's technical skills/expertise
Candidate's professional experience and achievements


Able to verify key claims the candidate has made on their cover letter/CV about what they did in the relevant role

Candidate's transferable skills (communication skills, teamwork etc)
Candidate's general work ethic and behaviour
Able to verify any extenuating circumstances that may affect the candidate's application (if relevant)


This means that the best formal references are from people the candidate has worked closely and consistently with over an extended period of time, and generally from those in supervisory roles. Your committee are precisely the people best placed to provide act as your referees. In terms of other good referees, if you've been, say, particularly involved with the teaching of a particular course, the lecturer you worked under may also be a suitable referee. Again, it's a similar sort of supervisory relationship, where they'll be able to make judgements of interest to a potential employer.

While it is sometimes the case in academia that referees with a looser connection are used (e.g. viva examiners), particularly to testify to the candidates academic knowledge, I'm not aware that this is hugely common. Most potential employers would expect to see references from supervisors; if those are absent, it's a huge red flag.

The real benefits you want to unlock from wider collaboration stem from the networking opportunities (although your primary purpose in seeking the collaboration should always be the overlap in research interests and potential for a strong shared project). Perhaps they'll be impressed enough to employ you, or they'll point you in the direction of open positions that they know of. They may well be willing to provide you with introductions to other PIs, that might grease the wheels of a job application.