Furnished premium is $700/mo but my turn costs are eating half of it

Your model is built correctly and the answer it gives you is correct for a $1,600 unit. The furnished premium is roughly fixed in dollars while the frictions are also roughly fixed in dollars, so the strategy works better as base rent rises. At $1,600 base, a $700 premium is eaten alive by four turns. At $3,200 base in a market where the furnished comp is $4,400, the same $250 cleans and the same 40 vacant days consume a far smaller share of a much larger premium.

Two lines in your model are worth attacking before you conclude anything. Ten days of vacancy per tenant is a sourcing outcome, not a law of physics. Operators who keep a waitlist with the two or three travel nurse agencies staffing their local hospital, and who ask outgoing tenants for referrals, run overlap or near-overlap and get that number down to three or four days. Do that and you recover $2,000 of the $3,000. The other line is stay length. Four tenants a year means average stays around 78 days after vacancy. A 13 week nursing contract is 91 days and extensions are common, so three tenants a year is achievable in a hospital-adjacent unit, which removes a full clean and a full vacancy gap.

The thing your model doesn't price is variance. A long term lease at $1,600 is a boring cash flow you can forecast. Mid-term at $2,300 with sourcing risk is the same expected number with a much wider distribution, and the bad tail is a unit sitting furnished and empty for two months while you pay utilities on it. If you're taking on that variance for $1,500 a year, you're being paid badly for it. Either find a market where the premium is proportionally larger, or don't furnish.