Don't know if I'll be much help but I kept thinking about how you could do these burst given you're time fram. I had a little royal icing left over from this weekend so I thought I'd play around a little to see if I could come up with something to get you through.
Here's a couple pics of a couple bursts that I made up really quick (so they're a little rough).
First royal icing has to be REALLY stiff. I used a Wilton 101 tip. Had the wider end against the paper and piped a base and then reduced pressure and pulled back to a point and repeated all the way around and then again to center.
These bursts are not as pretty as the flowers on the cake, but they at least have the points you're looking for...??? Just trying to help out a fellow caker!