Questions about what to with a stray dog taken in

Sorry about a weird title, but the automod really doesn't like discussing of animals that we happen to find

This isn't my first rodeo, but every dog is different, and I always kind of wing it. Apriori first thing I do is check for tags/chip, but most of the time they don't have any. Here is a list of my current problems, in no particular order. Keep in mind that I can't keep the dog, my house is full full.

Spaying/Neutering: This time it's a young unspayed female, that just went through a heat cycle. What do I do? Humane society isn't answering their phones or web requests for a spay appointment. My vet is charging something like 600 bucks to start. That's well out of my budget.

Finding her people: I posted on nextdoor, facebook, ring, pawboost, petcolove, and reported her to my city and county. Noone in the neighborhood recognizes her. Anything else I can do?

Finding her another home: How do I even go about it? My previous finds went to breed specific rescue groups, coworkers and friends. Well, these aren't an option here. Now what?

And any other useful advice, I am all ears.