I'd say give the Code Monster plan a shot, especially since the 1/2 off sale is still going. If it's not enough, you can always upgrade to Strictly Business. Upgrading and downgrading plans isn't a problem--that's why I'd start with the one that's currently the best deal.
If it can't be done at Dreamhost, it probably can't be done in a shared hosting environment. If that turns out to be the case, it should be easy to upgrade to dedicated, since theirs even come with the same control panel installed.
Save $96 at Dreamhost with the 96DOLLARSOFF promo code.