I see suggestions to use Zapier to collect from and post to the CMS; how would you do this if didn't have a budget for new recurring expenses?

Anything that zapier does can be done with custom written code (javascript), zapier makes it easier for us non-coders to do these things. I do agree that zapier’s plans are a bit costly considering how it’s a go-between between other services you’re already paying for.
I’ve used integromat as well. It’s a bit clunkier and takes longer to figure out but their pricing is more appealing.