Have you been able to see the inside of the unit? What condition has the tenant been keeping it in currently? I understand that others would double down on getting that deposit and going forward you definitely should as well as include a clause about canceling the lease. However, in this situation, if the tenant is keeping the place in decent shape as, I'd try to work with them. There's such a gray area with what can be deducted that anything short of blatant tenant damage, we just refund the deposit. It's not worth the hassle for us that a tenant fights over $100 repair deduction (speaking generally). Plus, you couldn't use their deposit to cover the vacancy they left you with anyway if nothing is currently in your lease.
When we purchased a SFR that came with inherited tenants, they were in the middle of their lease and wanted to extend immediately. But, we explained to them logically but firmly that we didn't underwrite them originally and weren't comfortable signing up with them for 12 months. Instead, we sold them on the idea of using the remaining period on their current lease as our underwriting period and with no hiccups, we would sign a new lease with them. They're about to renew their second lease with us and it's worked out fine. I would explain to the tenant that you have no intention of removing them, but that your motivations actually align with theirs pretty well, it's easier to move and it's easier to fill a vacant unit both when the weather is nicer, hopefully that can at least get them to the end of your six month term where you can reassess if they want to stay or go then.
Cameron