Sparkly……….
No, I would not recommend it. NCSY is an organization that functions best for members who belong through their teenage years, not join in college. A newbie in college would feel totally out of place. It is not the purpose of the organization to serve that demographic.
In my day the MO organization serving college students was Yavneh (I don’t believe it exists anymore). Very,very few NCSY girls get married within a year of ending being a teen (and certainly most not to Yeshiva bochrim). You say you are more on the MO side, but you appear to be to the right of most MO.
I’m sorry you have not found the right group to volunteer in Kiruv efforts. I think you should look for a non-membership based organization who does not develop its own leadership so you will not be automatically excluded.
Try volunteering at events hosted by NJOP (National Jewish Outreach Program) they are a dot org, not dot com and you can google their website for contact info