Oddly enough, that's about the process I follow. Normally I email two months before end of lease, this year between a new job, trying to buy another rental and grad school, I was a bit slower to get to it. Earlier this morning I emailed them essentially what you said above (though I had not read it at the time).
I told them it's fine to stay until the end of August, that I will be advertising the place and might show to prospective tenants with notice, and that I would be stopping by soon to checkout the interior to see what I need to do to turn the place. My add on CL had completely disappeared, so I had to post from a new one but I used verbiage from another post that was expired but still visible in my account. Had two respondents within an hour. I even raised the rent $50 in the post. Oh, and I also noted that their last months rent carried forward from their first year and since they already paid for July, no need to pay for August, and that their security deposit will be refunded shortly after move out - pending move out inspection.
I actually sent them that right before I posted my second post in the thread. It just made sense to do it this way, and seeing your post, reassures me. Ah, I miss that old house too, looking at the pictures of it in my advertisement reminds me of when I lived there for over 2 years in my late twenties. My first house, paid in cash. I had a lot of memories in that house. Learned a lot about home ownership. The journey continues.
I honestly do care about these people, I just wonder how they will turn out years from now. Looks like they'll be moving in with family after a divorce; save money, finally get ahead.