Sounds like a series of skill challenges. Maybe break up the floats construction into 3 stages (3 skill challenges) - the base and frame, the building onto the frame and finally, all the awesome decoration.
Acrobatics - climbing around the construction to help.
Athletics - Holding down parts, putting parts together.
Conspiracy - Using/finding/creating a plan to build it (bonuses to other skill checks)
Insight - How best to use any plans/materials (bonuses to other skill checks).
Interaction - Encouragement! (bonuses to other skill checks). At the end, go into the crowd and gain support for the float.
Mechanics - Best for stage one and two.
Nature - Discover the best uses for materials (bonuses to other skill checks).
Perception - Fine detail, the best decorations ever for the final stage.
Science - Most effective way to use your resources and construction of stage one and two.
Stealth - Go in the crowd and bolster the cheers without detection.