Make sure you let them know if you are performing any of the work, or if the repairs will ALL be made with contractors.

Verify income, credit score, and perform a background check.

I imagine going through sites like city data (although data here seems two years old) that has extensive data that goes through age, employment/unemployment, crime rate, etc.

As mentioned above you could just act as lender and record a mortgage/deed of trust with promissory note and personal guarantee from all parties in the deal would be the cleanest way to structure the deal.Another option which could potentially yield higher returns on your money is to become an equity partner in the deal, this could put your money in a riskier position and in the case of a default or failure to perform of other partners. 

My current builder has been not performing on a project I have and it is clear they are not doing anything to change their posture and improve or make up schedule.

Having a poor understanding of business, contracts, state and federal laws, negotiations, maintenance costs, etc. will continue to result in poor performance and finger pointing on both sides of the table. 

I think trying to keep it all is a stretch. 

Their work performance sucks. 

You indicate you know the law (assuming including the rent control law), but here are some thoughts:You can only legally terminate the tenant for a rehab extensive enough that tenant cannot occupy unit or to move in close family if your lease indicates that moving in family member is a reason for tenant termination. 

If they can't/won't accept the increase, they'll move on and you'll find someone else.I don't play around with incremental rent increases stretched out over time.