But when people are in difficult and desperate situations they will get scammed.  

You learn if they show up on time, if they bring someone who speaks for them instead of being able to speak for themselves, if they show up with an entourage that reeks of pot, you can walk them out to their vehicle to see if it's full of trash and filthy, if they smell of smoke, if they are a couple and argue about everything loudly, if they have screaming, unruly children, if they don't ask about normal things like where is the laundry, what's the parking situation, how big are the closets...all things that point to someone desperate.  

Unless you're desperate for the cash flow, the units that haven't taken the best care could get jacked up to market price and maybe it'll cause them to move.

So, the ones that are responding to your ad are more likely to be desperate tenants you probably don't want.Yes, you may end up having to wait for a new tenant to give 30 days notice to their current landlord, if you wait to show it when it's ready - but, those are the kinds of tenants you want. 

Why is this tenant desperate? 

If you have weird, unreasonable terms, you will only attract applicants who are so desperate, they will agree to anything in order to get housing. 

I'd change the no excessive late payments to no more than one late payment - otherwise, it's too subjective.You can add lots of other things like - smelling like smoke, rude behavior, unruly kids, bickering adults, adults yelling at kids, showing up with rude friends, filthy vehicle, having someone other than applicant who is doing all the talking, showing up late, sounding drunk when they leave a voicemail, not filling out application completely, asking for lots of changes like new carpet or paint (they'll be difficult to deal with), tenants who never ask where the laundry is or look to see how big the closets are or ask about parking (they are desperate to take anything), not bringing documents when they said they would -- the longer the legal list you have, the better. 

It took us a couple of months to get a tenant and had to go as low as $900 in rent as I desperately needed someone to start covering my mortgage ASAP.

.… when in Rome to what the Romans do.So, first Biggy is it overpriced that is number one reason.Winter time is always slower than spring /summer don’t get desperate and take a dude.

Seems to me you are messing with people who quite possibly have fallen on desperate times and are inviting them to retaliate.