I would suggest installing a copy of DadaMail
(free) on your shared hosting account, then invite
your forum users to subscribe to your newsletter. Do not
just dump all your forum members' emails in, that would be spam. But if you invite
them, and they double-opt in, then your list is 100% A-OK. (And you know the people on that list are really
interested in your site!)
With Dada Mail you can set any size batching. Set it to 6 emails per minute
. Yes, six
that will send out 360 emails per hour ... and leave you 140 emails/hour left over for ongoing forum notifications, etc.
That way you are well under all the limits, but your message makes it out.
Generally when I send out my newsletters, I batch them at 15/minute, and that puts no stress on the server whatsoever ... I like 15/minute because multiple accounts can be sending newsletters simultaneously and the server doesn't struggle with it at all. Both DadaMail
I know 15/minute is higher than HostGator will allow; I'm just explaining that that is a reasonable rate for a server that is not overloaded.