Sure, a conventional mortgage IS the best game in town.
But the house has to be in working condition to GET a conventional loan.
Should you have the repairs made and THEN embark on the major reno? Maybe. It's not the most economical way to do it from a construction standpoint but it might be the only way to avoid rehab loans, multiple closings, multiple appraisals and refinancing to an end loan (and all the expenses this entails).
Under normal conditions I would advise you to take you cash out in either a cash-out first or home equity line of credit (HELOC) not telling the lender that you are planning a major reno. But you can't do that with the house damaged.
The lender doesn't really care if you are only doing kitchens and baths or other major "upgrades". But they get involved if you start messing with roof changes and foundations or major exterior wall moving activities. They want architect/engineer plans and they want to disburse funds on THEIR schedule so they are not on the hook for uncompleted work (see: hole in the ground where their collateral used to be and a contractor who skipped town). Note: This is how things work in practice but I suppose even gutting your kitchen might technically violate your mortgage agreement by "affecting the home's marketability without the written consent of your lender".
Is not telling your lender your true plans a little shady? Sure, maybe. But it's not like you are doing a tear-down - lenders don't like it when your client tears down their collateral and sometimes neighbors snitch. I've heard of that happening once to a colleague's client.
I once put a HELOC in process for my brother who needed a little extra money to finish up an addition he was putting on his home (he's a contractor). I made the mistake of saying the word "addition" - DENIED. Oh did I say addition? I meant screen in his back porch - APPROVED.
Maybe the only above board way to do this is to have your lender make a rehab loan for you and release the insurance check as part of the disbursements.