Block time combined with Dicey's gc suggestion sounds like a good idea to me. Just don't make it an open house and limit it to couple people at a time.
I had a landlord who did that 2 weeks before we moved out and demanded the apt to be neat and tidy. Mind you we were trying to move and our stuff were literally all over the floor!
There were almost 20 people showed up and the landlord were outside most of the time busy talking with some people while other strangers roamed around our place.
One hour in, I realized the $2000 cash laying on the stationary cup on my bedroom desk. My point is, people are trying to move, stuff will mostly be unorganized with valuables in easy places to grab. Try to be considerate (which I can see you already are by trying to find the right thing to do).
Also, if your relationship with tenant is less than perfect, might not be a good idea to let the potential tenant meet the current one. Some people asked me how it was staying there (the old apt), I really wanted to tell them there was a reason why we moved but I figured it wasn't worth my time (landlord stop fixing things, loud after hour, charging cleaning fee eventhough we would clean it up and no damage).