Ginkgo Combination Puzzle

This is a little puzzle I invented (or at least I'm ignorant of other versions). The object is to rotate the pieces to produce a given pattern. Mathematically, it’s in the class of “2 dimensional combination puzzles”. I called it a ginkgo puzzle because the pieces remind me of ginkgo leaves.
A relatively easy challenge is to place all the pieces pointing in one direction, then rotate pieces until all the pieces are pointing in the other direction. A more complex challenge, which I haven’t done yet, is to place all the pieces pointing in one direction, then rotate pieces until half the pieces point in a direction at right angles to the original pieces.
Even though it can be a very simple puzzle, I find it fun to just turn the pieces.
I've posted a video of me playing with an earlier version of this puzzle at https://youtu.be/yhvrXx4ZLu4
There are 3,625,093,120 unique, valid (non-overlapping pieces, no mutually-dependent loops) board layouts in this puzzle. I've posted a program that calculates that number, at https://github.com/bneedhamia/GinkgoPuzzleEnumeration
The next question: how many of those 5.4 thousand million layouts can be achieved by starting with all pieces pointing up and turning pieces?

board.stl is the playing board. piecePrint25.stl is one playing piece – print 25 copies of this piece. Print without s or brim. Print as oriented in the STL: with the board pegs facing up and each piece’s handle facing up.
To assemble the puzzle, place each of the 25 pieces on a peg in the board, each piece pointing “North” (away from you).
I successfully printed this design in PolyLite PLA on my Lulzbot Mini printer, slicing it using Cura Lulzbot Edition set to the Lulzbot Mini Standard Resolution.
GinkoPuzzle.FCStd is the FreeCAD design file. I created the design in the Part Design Workbench, then used the Part Workbench to create the Refined copy of the board and piece for printing. I also created 24 copies of the piece, just so I can illustrate various board layouts – do not print these 24 copies.
The spreadsheet named “input” makes the size of the board and pieces adjustable. pieceRadius is the radius of each piece. pegDistance is pieceRadius plus a little clearance, and determines the size of the board.
In the Sketches I used links to external geometry to minimize repetition of measurements. For example, the piece’s SketchHandle makes a reference to an arc in SketchPiece so I could position the handle relative to the edge of the piece.
I used the MultiTransform Feature for the first time in this design. I used it to create the repeated peg patterns, and to create the repeated decorative edge pattern.
Once I’d created the piece and board in the Part Design Workbench, I switched to the Part Workbench to create Refined copies of those parts, for printing, and to Check Geometry. In the past I’ve found issues with parts that don’t appear until I make a Refined Copy and Check Geometry of that copy.