Believe you will find that when dry glazing putty is too delicate for this since they hang down and can be easily bumped or knocked off.
Your looking for something catalyzed and hard like the original finish
It seems like a good 2K primer would do the job. It'll spray nicely (and should run fairly easily) when wet, but will be pretty hard when it dries. Maybe even an epoxy primer would be better, though I'm not sure if it would sag or run as well as 2K. I'd think epoxy would be stronger when cured, though.
The tough part will be thinning the primer to where it will successfully and controllably run when you want it to, without messing the mixture ratio up enough that the primer never fully cures or hardens.