This completely sucks. It seems extremely unprofessional to remove a service when your alternate "solution" is still in beta and can't even accept new users. My only conclusion is that Dreamhost would rather we leave than to deal with the 0 support requests I made concerning administrator access.
I looked into Elastic Compute on Amazon Web Services. As someone else said, it seems a bit fiddly to get everything setup the way you want it, but it certainly can be done. The price for the first year looks pretty good, ~$5/month, but goes up to ~$15 /month in the second year.
In the interim, if you want to make it difficult for DH to remove your sudo access you can prevent them from logging in to your VPS. I will caution, this will mean that the Dreamhost panel will also not be able to make changes to your configuration. You really will be completely on your own to manage your VPS, so be careful.
But, if you log in to your account as an administrator and as root rename:
To something like:
The Dreamhost panel and dreamhost support will no longer be able to SSH into your machine. Of course, they can still simply turn off your VPS, and with direct access to your storage, they can make modifications to your filesystem without needing SSH.