Question about INSURANCE....

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I have a call in to my insurance agent but thought I might post something here in the meantime....
I am about to obtain my first SFH investment property "subject-to" and I want to make sure that I have my liabilities covered. I have flipped/purchased properties in the past but they have all been straight purchases (so I arranged the typical HOI coverage). The previous owner carries standard HOI and a conventional mortgage which will still be in existance for the next 60-90 days (assuming all goes well with the rehab/resale). My question is what type of HOI should I secure to protect my new investment? I assume if lightning strikes the day after I take over the property, the only person that will receive the claim proceeds will be the lienholder and then I'm left with a hole in my pocket. Can I put a 90 day policy on the home? Is there a way to lower my costs so that I'm not paying 3 months' reserves, start up fees, etc. on a traditional policy? I'm sure my agent will tell me to just set up a regular policy, and I'm sure that's probably what I need to do....but I was hoping to find a better alternative that keeps me safe while also lowering my costs. Any thoughts?