MailChimp is a great EMS, especially if you use it as your canonical database for contacts (due to segments). Unfortunately, that’s not really how things work with Vin65 and I know for a fact they are hesitant to build integrations with outside services like this.
SendGrid is just a backbone for Vin65’s email platform. I don’t think there’s a problem there. Vin65 just needs to make some tweaks. But the bottom line is Vin65 aren’t email marketers, so if you want to take the next step, you’re going to need to use an outside EMS.