I don't know how long it takes for you to create a synth, but it may be worth making a time lapsed video of your process for two reasons:

1. It should satisfy etsy's requirements of displaying how it is handmade

2. You and your customers may appreciate the video (a little advertising)

I understand that etsy's request is unreasonable and the conversation with them, unpleasant, but I think this would be a solution. If the video is done well, you hopefully won't be giving away any secret sauce to your manufacturing process.

If all else fails, I suppose it would be time to find another community of craftsmen.