Hi Thu, I'm sorry for your trouble, it's a frustrated situation especially when you are a distant owner. I can relate because I also just bought a house on Roofstock too, in Indianapolis, and using the same insurance company as you (Real Protect). I highly recommend you to use your insurance to pay for the door if the cost to replace it is higher than your deductible. Remember you paid them for time like this, so use their service when you need it. Don't worry about the insurance increase, usually it won't be much for something this minor, you probably gonna lose the "no claim discount" at most, if they even offer it. I don't know how much of a renovation you did to your house, but if you think you did a good job on it keep the rent as it or increase it to the market rate; you want to get back your initial investment asap and buy another house. (Check rentometer and neighborhoodscout to see if your area have a high rate of rental property, then ask your PM to adjust your rent accordingly, PM love rent increase because they charge you on %)
P/S: if you decide to use Real Protect, please let me know how is their service. Thank you and good luck on your REI.