Should I include a contingency that says current tenants must sign a lease with me at or before closing, or is this going to kill the offer? 

I loves in a few during my undergrad years, it was nothing to have 250+ people in a half double 2 or 3 times per week for a little party, that’s just the norm in Stroudsburg.Parents sign the lease, renters insurance required, monthly checking, 1st, last and security.

This of course may not be in every case but if you not experience it will most probably turn out not really being in your own interest to attempt to do a lot of the work yourself or by using cheap unskilled labor. 

In may of this year I was going to increase the rent but I gave him a chose to pay $50 more per month or if he signed a two year contract I would keep the rent at $850/month.

They provided security upon lease signing. 

I am thinking your worrying about nothing.. when I create HOA's for my new communities I never turn them over to the owners until I am done building 100% of my project out.. last  thing you want to do is answer to a bunch of homeowners :)  then they set up their committees and they make sure everyone keeps the property in good condition etc etc. 

My husband and I are planning to buy a new smaller home for ourselves and turn our current home into a rental property.

My live-in tenants and I have not seen a single car at that house since the for-sale sign went up.

If the tenant has a lease that expired a year ago, (ie: nobody can produce a current lease), then you just need to draw up a new lease, provide a month's notice of the increase, and if she won't sign or move out after the 30 days, consult a real estate lawyer or file for eviction.

This way they have to sign up for Cozy.