As it happens there's an analogous organization at the national level, namely the Association of State Democratic Chairs (again distinct from the DNC, the actual national party committee) where the various state party chairs can likewise get together and commiserate on the woes of being a state party chair. But they do other things, too, like their recent endorsement of Howard Dean for DNC chair.
There's something wrong with this picture, but it took me a while to come up with the missing puzzle piece:
Other states undoubtedly have district/county chair organizations of their own. And naturally the various chair chairs (i.e., the chairs of those district/county-chair organizations) face rather interesting problems specific to those kinds of organizations, and doubtless some kind of experience/resource sharing and coordination would help there, too.
Thus, I propose an Assocation of Democratic State Legislative District/County Chair Association Chairs. The chair chair chair could then convene regular meetings of the chair chairs to commiserate about the various meta-aspects of being a district/county chair chair. But they could do other things, too. E.g., if the ASDC were to have a contested chair election of its own, the ADSLDCCAC could step in and make helpful endorsements.
which completes the triangle
LD orgs --- state orgs(WSDCC) --- DNC \ / \ / state DCCOs ASDC \ / ADSLDCCAC
Though, now that I think about it, when you consider the fact that the various precinct chairs have specific needs of their own, that within each LD/county org, there's someone not the chair who's job it is to deal with such and be sort of a precinct-chair chair (in our case it's the LD 2nd Vice-Chair), one could then see a use for a statewide association of precinct-chair chairs and then a national assocation of precinct chair chair chairs, headed up by a chair chair chair chair ...
precincts --- LD orgs --- state orgs(WSDCC) --- DNC \ / \ / \ / PCO orgs state DCCOs ASDC \ / \ / state LDPCOVC orgs ADSLDCCAC \ / ADLDCPCOVCAC
I think I can promise that my Reign of Terror, while no less horrible, will at least be different from everybody else's.