i must point out that the names of those commands are chosen a little confusing. for quite some time i assumed that project should do what pull actually does. not knowing all the commands and what they can at the first instant did not help much at all… something more or less minor to think about to whomever it may concern.
anyhow thats how project would look like but for this the curves have to be exactly above the surfaces you want to have the pattern on but its very limitted as pascal wrote only perpendicular to a cplane. you can of course make a new cplane rotate it as you want and use this as a projection method.
another option is pull. for this you target the curves how you want to have them “projected” along the surface normals of your polysurfaces. this computes a little longer so depending on the age of your computer it can take a few minutes, at least on my old mac it does.
you also have something like FlowAlongSrf but this only works on a single surface and not on polysurfaces you have there. has the advantage to follow the exact curvature of a bent curvy surface.
oh and by the way your objects are far off grid that can cause some issues. i would put them back in place with boxedit and center them on the cplane again and shrink them down a few numbers, they are far too big either.