It's not impossible at all, but you have to be a little creative.
You can manually add subscribers to your list from the Announce List management page, in the form of a list of addresses. Just browse to your Control Panel -> Mail -> Announce Lists and click the "Edit" link under the "Actions" column of the rows for your Announce List.
On the next page, scroll down to the "Edit Subscriber List" section, and paste your old list of names/addresses, etc there, in the format described.
You can get your "exported" list from your other program into the correct format, suitable for copy-n-pasting, in a number of ways ( a perl script, a series of Search/replace operations on the file, etc.).
That said, remember that DreamHost's Anti-Spam policies treat this as a "new" list, and you will need to repeat the "confirmed opt-in" registration of all your users to be in compliance. If you don't do this, a spam complaint will very likely result in you being found to be in violation of the Anti-Spam policy and the TOS, and it could put your account in jeopardy.
Of course, that's the same risk you might run using the old software, so you will have to evaluate that risk for yourself.