About putting affiliation on a paper or not
Affiliations are about finding and positively identifying you, as well as also understanding your approach to the problem.
For example (and this is a real case), I would put much less stock in linguistics papers authored by people in the economics department than linguistics.
In the US and Canada, institutions derive so little value from having their name as your affiliation, I don't personally see much of a point in not putting the institutions you're currently at to &quot;stick it to them.&quot; In any case, having a real affiliation looks much better than &quot;Independent Scholar&quot; (perhaps unfortunately).
Commenters indicate this is different in other systems, which I'm not qualified to address. Nonetheless, I would err on the side of including them; not only because of your quote below, but for the benefit of the community and improving your own credibility.

besides having access to some database of my field and access to journal papers

This is not nothing. I would recommend putting the colleges you currently teach at. If they no longer employ you at the final check, take them off.