One thing I won't do is compromise my selection criteria.

That should be a good compromise.

An acceptable compromise might be this: you may sweeten the deal with a carry back note, to lower the down payment requirements by ten percent, which could help a successful investor with growth they are qualified for, but don't have the full cash position.

Sometimes people get too attached to a property and they are willing to compromise on what they want just for the sake of getting a  dealBeing able to "NO DEAL" ( to a bad deal ) is better than saying yes to a bad deal, just for the sake of having something.When you analyze a deal, think to yourself, If i had 5 other deals on the table would I still accept this deal.If your only reason to accept deal is because there is nothing else on the table. 

If one or both of you are stubborn and unwilling to compromise on business issues, you can do some real damage to your relationship.Only you and your spouse can make that judgment, but on general principle, I'm not in favor. 

So, in order for the property to not be vacant, you may compromise and give it to a tenant that you would otherwise not be interacting with in a better neighborhood.

One compromise that comes to mind is to tell them they can do it but they each have to continue paying what they are currently paying until both units are rented or their lease expires, whichever comes first.

You have the right to enter any room in YOUR house, provided you give the tenant notice that you will be entering, unless it is an emergency, then you can enter right away. you have a right to those keys or to have the tenant remove them. if this tenant is so paranoid maybe a compromise of installed entry door handles on every door so that they are keyed alike. this way the tenant has locking doors and all you need is one key to open them all.

Compromising integrity should feel greasy and it's an attempt to make up for a lack of competency.

I personally wanted to do a 4 plex in a war zone for 2 years, but my wife wanted a single family home...the duplex was our compromise and it has worked out well for us.