Hi neighbor!
I don't have a reg to back this up, but I would think since you're dealing with a new property, new purpose, & new loan program (at least at our bank), it would be a withdrawn application for the HE & a new app for the purchase. That is how we would handle it. Since the only time restraint on closing a purchase loan is the 7 day period after providing the LE, you should still be able to close quickly - considering you get your appraisal back in a timely manner.