Well, you may not feel, or believe, that you are “spamming”, but list mailing without confirmed opt-in, irrespective of the software you use, is a violation of DH’s Anti-Spam policy (note “Subscriptions” section) so it’s not particularly relevant whether or not you call it “spamming” - DH prohibits it. Period.
Note, that even if you continue to “split up your emails” as your list grows that will only serve to avoid the quotas kicking in, and will do nothing at all to help your situation when/if you receive complaints from a recipient. The resultant investigation into the complaint will reveal you are not in compliance with the anti-spam policy, and you will quite likely find your account suspended or closed altogether (I do not work for DreamHost, so I will not say *certainly", even though that has been others’ experience).
All in all, attempting to circumvent DH stated policy on list-mailing is likely to work out badly for you, and if you really want to host on DH, I suggest you change your practices now rather than be forced (and probably at the worst possible time) to struggle to get your account re-instated (which they may not even do) and then have to change anyway or change hosts altogether. That’s just my opinion, which is worth exactly what you have paid for it, and YMMV!
DH does not currently offer plan-based exceptions to it’s Anti-Spam policy - even their dedicated servers share mailservers, so they have no interest in facilitating any behavior that increases those servers’ likelihood of being “blocked” by the spam-fighting organizations, ISPs, or other mail systems.
If you were compliant with DH Anti-Spam policy, you could ask for an increase in the number of mails you could send in an hour, and possibly receive such an increase, but that will not happen unless you use confirmed opt-in and comply in every other way with DH policy.
There are other things you could do via software (automatically queued sending, etc.) but those won’t solve your non-compliance problem. You are presently violating policy and getting away with it; I would not expect that you will be lucky enough for that to continue.
Why isn’t there a way for you to do a “confirmed opt-in”?
(btw - the term “double opt-in” is a term used by spammers, not knowledgeable and legitimate list managers or legitimate commercial e-mailers - you won’t help your case using that terminology, or “email blast”, etc., with DH)