Yikes this is terrible. 300 Emails should go out in less than 1 minute.
I'd say there is a grossly misconfigured mail or mysql system or something really really bad.
On my list of 150,000 I average around 30,000+ per hour with a fairly small message, 3-5k or so. It rarely ever stops during a mailing, even though it has stopped a couple of times. I'd love to see a background mailing feature instituted.