mass mailing solution??

I need to be able to send mass emails to about 1000 people and my hosting provider only allows 400 per hour.
Simplenews does a great job mailing via cron and I use it for newsletter. However, for other emails I've tried to use Mass Contact module and it didn't send stuff out, not sure why. If it's PHP timeout, combining it with Job Queue supposedly fixes this, but the issue of 400 email per hour still stands. I've also had to hack Mass Contact to allow filtering recipients by profile fields, like when you need to send an email to people in a given state.
Looks like lots of people may need these features. I can't believe nobody has created yet a workable solution, based for example on improved Mass Contact for creating emails and Simplenews mechanism for sending them out. I would have tried myself if I only had time. But maybe there's already a project I'm not aware of?