Suggestions needed - announcement emailing

I have an announcement mod installed on my forums, that flags specific boards to be announcement boards - any posts in them being exported to the portal and rss feeds. However I was wanting to automatically email a copy of any posts in these boards to members, to alert them of new announcements/news (obviously having un-subscribe options & what not, the aim is to inform not to spam).

Writing the mod wouldn't be any problem, however I could do with some help designing it - My forums have over 3000 members = 3000 emails per announcement (announcements aren't regular, 1 or 2 a week at tops). Obviously though sending 3000 emails in a simple loop is not going to go down well with the mail server. Not surprisingly actually my host's TOS states you can send a max of 200 emails an hour.

One solution that came to mind would be a email queue and some kind of script on crontab to send 100 or so every hour, but that seems kinda messy, and I'm pretty sure the host wouldn't be too happy with it, even if it is within the TOS.

Would simply using a SMTP server hosted elsewhere for my emailing be alright? Or would sending 3000+ requests to the external mail server still be a bit much? (My knowledge around email is fairly limited, it's not something I've had to deal with before.)

PS. I'm not sure if this is the best board for this, the context is PunBB but the question and problem themselves aren't - feel free to move.