I'd check out
Mandrill. My company uses MailChimp which is a sister (or maybe parent?) company for our email subscription lists. Mandrill is more for 1-to-1 emails, transactional emails (your order's been shipped!), and the like. They have a comparison to SendGrid
here.
Unfortunately I've only just started to use them as we're looking to start sending out marketing automated messages for our customers to follow up with them on their experiences after a period of time. I haven't had any complaints about the service so far, but it's still early on.
I think that they would fit all your listed requirements. Their pricing starts at $free for up to 12,000 emails a month, $.20/thousand for the next 1m, $.15/thousand for the next 5m, and $.10/thousand for any higher, all of which appear cheaper than SendGrid.
I definitely know that they handle blacklists for people who have opted out. I'm not positive of what you're looking for with regards to batching but they do throttle your email send rate based on your overall reputation. Fewer complaints and clean recipients, faster rates...more complains, bounces, whatever slower rates. But they handle all the queuing up so you just send them as fast as you can and they handle how fast they get sent out.
I haven't had to use their technical support so I can't comment on that, however I have use MailChimps and it's always been excellent. We've had 2 or 3 incidents where complaints prompted an "investigation". In all the cases they were very prompt with responses, worked with us to get to the underlying cause, and in all the cases had no problem as we were doing everything right. I can't fault them for trying to keep their reputation clean and monitoring for potential spam-related issues. And during the investigation they weren't very punitive as well.
Edited to add: If you are a MailChimp customer already (or become one), you get additional twice as many Mandrill emails as what the upper limit is of your MailChimp plan. For instance, we're on the $75 5,801-10,000 plan for MailChimp. So we get 20,000 free emails + the initial 12,000 emails. That's easily more than what we'll regularly use so we basically get Mandrill free just for using MailChimp.