Tenant Screening Dilemma: HUD-VASH vs. Terrible Credit

Good morning! I'm screening for my first SF rental, struggling with a decision, and would appreciate some feedback.

The candidate I like best is a single mom with 4 well-behaved children. She seems to have a pretty good head on her shoulders and gives me the impression that she'll take good care of my house and be an asset to the neighborhood. She's also a disabled vet and will be using the HUD-VASH program, which covers 70% of the rent and will be paid directly to me from HUD.

However, her credit is a complete disaster. She was very upfront and explained all of it as being related to an ugly divorce. She showed me her last 12 months of rent receipts (1 month was late) and bank statements (which show income that meets my minimum criteria). The other zinger is that she is being evicted, with a plausible explanation: the AC went out several months ago, the landlord didn't fix it, and when the Houston heat kicked in, she took it upon herself to get it fixed and chose not to pay rent to cover the cost. She's now evicted as of August 1.

What are your thoughts about renting to a person like this? Would bad credit and an eviction trump guaranteed rent payment and a good fit for the house/neighborhood?