Defiantly do the routine screening of the students in addition to the full screening of co-signer including the full credit /background check.Based on the description of the tenant issues you had and the fact that they were students I would suggest that you did not fulfill your responsibilities as a landlord.

Make sure the tenants know you will be checking on the property routinely. 

Do you send inspections to banks routinely as a requirement?

So basically everything else is on the tenant.Are you asking to specify that the tenant must hire pest control on their dime on a routine schedule?

Given the property is in demand, you do not need to keep a tenant who you do not trust and on whom you will need to routinely check.

I give weeks of notice for any routine maintenance.  7 weeks for the last boiler maintenance, with a reminder the week before.  

schedule a routine inspection of the interior in the next month.

Jay my routine flying is like rain man.

Please note that changing the AC filter and cleaning the AC air intake closet should be done once every 30 days as part of routine maintenance.The Air filter on the AC had not been changed since you first moved in (Dec 2015) and the new replacement you bought was not the right size.

BTW, I routinely have county officials tell me that their placed applicants "easily" meet the payment qualifications for our efficiency apartments. $525 rent, $733 SSI payment.