Not sure if this helps at all, but I diagrammed out what I could, based on

http://www.mathstat.concordia.ca/faculty/pgora/m475/Gosper%20Island.html
and
http://www.fractalcurves.com/Root7.html

I'll post it in binary images.
That ought to give some basis for proportions and angles.

Looks like you've got L (black line), L/2, S (hexagon side), S/2, 90 deg, 60
deg, 120 deg, 45 deg, 15 deg, 75 and 95 deg (on either side of the orange line)
to work with.   Plus whatever relationships there are with hexagons with lines
from center to vertices or edge midpoints.

I've been banging my head on stuff here all day, so I'm probably calling it
quits for the night.   I'll check in the morning and see if you figured it out,
or if you can give me something to take up and run with.

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