I am all too familiar with being in strong winds jibless. I've made some tacks going backwards and reversing the rudders, but usually I'm just too impatient for that
so I opt for the jibe. I generally wait for a calm in the wind, get aft, head downwind with speed then get leeward just as the sail is about to catch the wind and push it over before the wind does it with violence. The thing that really stinks about this is having a obstruction on your downwind that you didn't plan for. ( like running out of room because of two failed tacks)
Kinda funny, a few weeks ago there was a small craft to my downwind and soon as I could clear him ( both going in the same direction) I circled him in a complete 360 with amazing speed. He looked in astonishment and was laughing about the maneuver. Sure glad he thought it was cute, because I didn't want to be the asss who slammed into moored boats.