They may have bumped it up a bit due to seattle's "emergency" blanket ban on screening for eviction or nonpayment history.I would drop your asking price before relaxing your screening criteria.   

If you are confident in your tenant you will relax more.

They won't be able to ever just relax, if they never know when you're coming and that window is a 12 hour window every day.So, make it a 2 hour window, and less if possible.  

One bad tenant and you will realize that you were too relaxed.

But, since you're on a month to month contract, if you want to leave, you just have to give 30 days notice.Then, they (the complainers) will usually find a few maintenance things they want fixed, just to flex their muscles a bit, which we would take care of, and then everybody calms down again.I also never had anyone move over an increase.  

In my experience (and this is admittedly probably more of a concern for multi-family properties), sellers have an incentive to relax their tenant screening requirements in order to get the property to "full occupancy" so they can advertise a higher cap rate.

I know how you are feeling but good thing is your current tenant is move out but can't find mover so help current tenant in finding mover.Secondly, you should have in the LA that, if the new tenant can not move in X days then they should change the lease date or terminate the lease date.Thirdly based on the current tenant situation inform new tenant about your current tenant problem.Just relax and all will be fine!

first off you need to relax and remember this things are part of RE business. 

Plus, if you allow them to get you involved in their problems, and then you relax some rule because of their problems, then they can end up taking advantage of you.You'll get the hang of it. 

I never sue in small claims court, landlords don't respond well when they aren't forced to pay a lawyer (small claims relaxes the procedures and lawyers are not often necessary.)