You could try the commercial growers listed on the AGGS web site. Go to www.aggs.org, then go to the bottom of the Home page and click on "suppliers".
As for other tuberous genera, there is Chrysothemus. It grows in lower light than Sinningias but needs high humidity.
For rhizomatous genera, try Smithianthas, Diastema, Heppiella, Lysionotus, Kohleria. These should keep you going for a while! Diastema grow in similar conditions as Achimenes; Smithiantha can handle cooler temperatures and higher light, as do Kohlerias. Lysionotus has smooth rhizomes, prefers low (semi- shade) and tolerates cool temperatures very well, as does Heppiella. Heppiella needs the same humidity as Diastema to grow well. Otherwise, they get very leggy.

Marilyn

Would appreciate some recommendations of sources myself. I've found that things I've grown from rhizomes are more likely to do well under my conditions. No shock from plants being moved here from a greenhouse.