Here’s roughly the reason that the “Like” button is being pushed into your syndicated copies: https://github.com/Automattic/jetpack/issues/4399
Ultimately, I decided that very few people were using that like functionality on my site (which is WordPress specific), so I just turned it off in JetPack to “fix” the problem. There are other possible methods to fix it within your theme, but it will ultimately be very hacky based on my past attempts.