Spoiler:
height = 10.0 mm
outer diam = 11.5 mm
inner diam = 10.9 mm
wire thickness = 0.30 mm
full compression height = 0.89 mm
number of coils = 4
force required for full compression = 15 grams @ 1 x g
The spring is flat on top and bottom.
Might such springs be harvested from old keyboards? I think there were BTC boards with foam/foil switches that used springs under the keycaps, and I think the Commodore 64 keyboard used a Mitsumi switch with an external spring that might be suitable.
Other suggestions welcome!