Are enewsletter and thesis incompatible?

I'm having a bizarre issue I've never run into before with one of my client's sites:

I moved the site to wpengine hosting a couple of weeks ago, and since the move the site has been ridiculously slow in the back end area.

I've talked to wpengine tech support about it, and here's the latest message I got back:

"I'm looking through your MySQL log, and it looks like I'm seeing a lot of slow querires coming from the eNewsletter plugin you have installed. The log was a bit long, so I've attached it as a text file to this ticket. I would take a look at other solutions for newsletters than something hosted within WordPress. We really don't recommend doing it this way anyway, since our servers aren't setup for sending mass email. I recommend Mailchimp. It's free, and a truly great product. Take a look, and please let us know if you have any other questions."

The site was built with Thesis and some big fat customizations, and I was wondering if the most recent e-newsletter plays nice with Thesis? Could that be the issue? Halp!

Thanks guys.