Multiple websites under the same Google account - Can it be bad for SEO?

That is one of the great mistakes that you have done buddy. I will tell you for free that from time to time, there is cross checking that happens. You will therefore be able to suffer in one way just because the other website suffered. Especially now that you have issues with the black hat, they have higher chances that you are using so in the other website. Consider shifting that for your own benefits.

In my experience I've got penalized all websites in Google account, even white hat and client websites. Since then I use one Google account for one website.