But I'd still want to do the tenant screening/approvals. 

Trying to collect a judgement from a section 8 tenant is squeezing blood from a stone.In general judgements will show up in the public record, most tenant screening services will find it.

Do you have any screening requirements that are turning prospective renters off?

There are a number of tenant screening services that do this for you for about $15 to $25.

If they wish to continue living in the unit after the price increase great (be sure to screen and ensure they can afford the new amount). if not, let them know you're sorry but the arrangement isn't going to work out.

Ideally they would have to answer my pre-screening questions prior to even setting up a showing. 

Why I haven't taken the plunge yet to actively searching or formulating anything, (kudos to you for acting) knowing what you want, comparable cap rates and estimates of cash on cash returns would  give one a quick filter to screen out properties before looking.

Hello BP people,As I'm working to put together my process for tenants selection there are a couple of questions I would like to have your feedback:If you have a couple as potential tenants, do you make both of them to...

I understand that a good screening process can make a huge difference. 1.

Sometimes you are better if they move out and you get your own tenants, depending on how well the prior person screened them.