I went and picked up a silk rose.  The petals were the perfect shape, curved in two directions with a slight downturn of the upper lip.  They were also spaced and cut so that they should curve just like my nylon petals.

They were also glued together, to keep that shape.

Removing the glue from the silky fabric that is the rose has proven impossible.  So even if I did assemble the rose using these petals, I'm guessing that any data I would gather about the interfacing/sliding of the petals would be compromised by the remaining glue, preventing smooth action.

It appears to be hot-melt glue, so lots of flailing attempting to heat it and dab it off has happened.

I need clean petals, of that shape.  So far I have not found anywhere that has pure white rose petals, of that shape, which are not glued.

I may actually need to spend more than $3 to get them.

I have yet to visit an actual craft store.  On the agenda.