Now that it's August, I know they are allowed to stay until 10/1 because I gave them notice this month. 

I would assume that would stay true after trying to refinance after we have 20% equity?

They tend to stay a long time. 

Also, a reason not to accept a security deposit from a nonprofit or social service agency is because if you get into a conflict with the tenant, the organization will "advocate" for them, including legally, and may be quite absurd (and incorrect) about the level of "rights" they claim for the tenant, and this is super stressful, and also, now you have a very entitled tenant who thinks you're obligated to put up with all sorts of awful behavior- because they've been erroneously led to believe that they have excessive "rights."   

Let's stay in touch as guidance comes out

Also ask yourself, how organized are you?

In terms of living on the income my real estate generates (I have a job but not a very secure or reliable income job), would I be better off staying with the properties paid off or looking for similar good deals and mortgaging them ?

I'm a newbe who lives in California and I've been spending the last 4-6 months reading everything real estate related that I can, staying up to date on the forums here and listening to all of the BP podcasts that I can.

So staying all bills paid could be a bonus to your property.

I started attending this meetup organized by @Kyle Mitchelland it's great.