Do people with $400/mo for rent in your area have a lot of housing choices?

Check in your local paper and write to the local editor or reporter that writes human interest stories.

But the more gentle route will build relationship, which will serve you better in the long run.People always like to feel some sense of control over their own destiny, so present this as their choice... to stay with you by abiding by your rental terms or to find another place to live.

I give my tenants a choice and many use Venmo, some use Chase QuickPay, and others mail me a check.

. - Sounds like your choice to do this.

Your best choice going forward is buy the property at a "discount" based on the condition of the property, etc, giving the seller some amount of money (which serves two purposes, 1. he has no money and he needs money to make the move and 2.

If anybody out there hasn't listened to these Podcast I highly recommend them both, but then again, I recommend listening to any and all of the BP podcast (but these are MY INSPIRATIONAL choices). 

If you are of the opinion that you will have no other applicants you really only have two choices, hold out for additional applicants or accept this high risk couple and possibly be forced to evict.

Anytime by choice (or as outlined in the lease).

But you have about 2 choices in Portland now thanks to a completely lame ordinance  from a lame city council who want to keep tenants in their "homes" at all costs.   1) you can evict them on a violation of their lease (not paying, smoking, extra pet, noise, etc),  but they have they easily have right to stop the violation and stay.