Our experience has been that when bad things happen to good tenants - job loss, medical emergency - something that impacts their ability to meet their obligations under the lease, the good tenant typically comes to us before an adverse event occurs.  

If you make more than enough money to cover the $400 a month hit, and it doesn't adversely effect your lifestyle, then I don't think I can be too critical.

“HUD will use the full force of the law to protect the fair housing rights of folks who’ve been arrested or who’re returning to their communities after serving time in jail or prison,” HUD Secretary Julian Castro warned.By “full force,” he means the “disparate impact” theory of civil-rights enforcement, which HUD claims is written into the Fair Housing Act even though the phrase appears nowhere in the statute.Disparate impact holds businesses liable for colorblind policies and practices that may have adverse outcomes for minorities — in this case, screening all apartment applicants for criminal histories.

Someone acting on reliance of the information you provide could face extreme adverse consequences, and disclaimers will not always protect you.DISCLAIMER: None of the above shall be taken as comprehensive analysis of the law in any one particular state.

Assuming your information is complete, it appears to me that adverse circumstances befell both  parties. 

That said, I did call HomeForward yesterday to see if it would be possible to put these tenants on Section 8, and that way, if I raised rents to market, it would not adversely affect them.  

If nothing else, you will have a judgement that can be noted on their credit history.Something you might consider for the future: in the form we use to gain consent from an applicant to pull their credit history there is wording which also gathers their consent to report payment events (both adverse and positive) to the credit agency (this wording comes from the agency itself and is part of a template we are to use as part of the service).  

Despite the lease, does she at some point get tenants' rights (I'm thinking something akin to "adverse possession.") or do I have to option to consider her a trespasser if I choose?

If you get in front of a Judge or Jury, and either of them do not like you, the questions alone could allow for an adverse, non-appealable ruling.

There are lots of ways to overcome her picture not looking like her.Also I'd be worried about her stuffing the place with more people than what she is presenting to get more benefits.