Top wrap it. Set the action low and take all the relief out of the neck you can without it being a buzzy mess that frets out. Balance that bridge height and relief until it plays good. Lemme know how it goes. My Bigsby equipped Edwards ES is about the lightest string tension of any guitar I've owned until I top wrapped my Edwards LP. String gauges on both are 10 11.5 15 20 30 39, the bottom three are flatwounds.