Ok, so they didn't answer my email so my first advice is to get your hotel or a Japanese friend to book on your behalf.
The basic dyeing experience costs ￥4000 including museum admission. Postage to my country cost an extra ￥900.
At that time I was the only person at their well-lit workshop space. Staff was pretty friendly.
You get to choose a design, then select a base colour for the silk (pre-dyed).
After you have finished painting, they will do the final processes (like removing the paste sitting on the outlines of the design). The final product will reach you in about a month's time.
Overall, recommended. However, a detour to visit just the (small) museum may not be worth your time. They did allow me to take photographs though. Oh, there's a small gift shop too.
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