I have personally created an H1 tag in an image, I didn't see no negative effects. H1 tags are not as important but should be implemented, so even if it had any impact maybe it was minuscule.

H1 tags don't generally have to be visible like in my case, it was an H1 tag for the logo. I'm not sure where you are putting the H1 tag but if its an image I say why not, but if it is a regular text, why not just keep it as an H1 without hiding?

There is really nothing you can do because someone else is copying your description.

The only thing I can initially come up with is asking your dropshippers to not copy descriptions.

However, the content that is duplicated and might not really negatively effect your SEO. Google understands e-commerce and a lot of the times products on e-commerce sites are very similar and they do not get penalized. Another thing is that you originally created the description and Google does index according to freshness. As long as you are indexed first with the description, I don't see how Google can penalize you.