What would I have done? I'd have been off the route before the sun hit the face. It worked for the gracious folks that lowered you the rope.
However, from what we see in the vid, it looks as if you were attempting to get to top by the shortest route, via that patch of thin ice. I appears to me as if the ice to climbers right was a not as lean, a quick step right and up, you'd have made it clean. This looks to be exactly what you did once on top rope. Sometimes the shortest route isn't the direct one.
Otherwise, cleaning the loose, thin ice to clean rock, would have been my best move, given that it would not endanger my belayer, or others below.
Salvation from such situations can come in many forms. 25+ years ago, while walking along the base of the Trapps, I heard a climber named Don Hamilton recite a short prayer as he was leading up on tenuous pro.
"Oh Lord, please put Joel Ponti in my place."
In such situations, one must do , what one must do.