We have done it a couple of ways in the past... One way was to allow directors to "submit" plays that they wanted to direct.. This was usually in the neighborhood of 10 directors being solicited and each submitting 5 plays. This gave our playreading group some 50 plays to read and select from. Problem being that most of the directors only had one or two that they REALLY felt strong about and to get the other three it seemed like they had just scanned the French cataloge for snippets that sounded interesting... (many were not)  From those plays a well rounded season was hopefully selected (not always the case either)  Getting quality directors finally came to paying a stipend (currently 300 for a straight show and 400 for a musical)  If you haven't gone there yet, Dont. If you can at all help it, keep the camels nose out of the tent! We now pay Music directors, pianists, orchestras, producers, choreographers and the list just keeps growing. (to be fair, I believe we started paying musicians first as they have always been hard to come by.)  Currently, everyone (patrons, members, directors etc) are able to submit plays for review and our playreading committee selects what the colective sees as a well rounded season. Though some thought is given during the "process" who might be available, good at, or has submitted/championed a piece, our director stable, (currently about 6 or 7 perms and another 4 or 5 periferals) is solicited as to interest/availablitlity...  USUALLY it works out.. Do we wish we had more choices, you bet.  New blood can be a good thing.. But it works out..

This probably won't help you much Gracie, as we have less than 3 million people in the whole State [Which is supposed to be the largest State in the world. (1/3rd of the 1 Million square KM's of the Aussie land mass)]
I don't know any of the 300 or so incorporated theatre groups here, who pay any directors or production staff, mainly because the Model Incorporate rules preclude any member of a non profit group recieving payments.
Most of these groups have 3 to 5 productions/year, Directors in a lot of cases are from within the group or from other groups. Nearly everyone belongs to more than one group, especialy with the actors, who are like gypsy's & nomadic, moving between groups chasing parts. The same with Directors, who use the the local Independant Theatre Association [Aunty] 'Theatre Australia' web site & network  around the traps to individual groups.
We find  it better to cultivate our own Directors, as we can always find diamonds in the back yard.
With the groups that have thier own theatre to play in, more & more except productions from other groups so they don't have the venue black. Either as a complete Bump In show or just the production team, using local in house members for the show, which is becoming the norm these days.
In the Bush towns they draw upon the influx of young teachers from the local schools a lot to boost  thier production teams. Which in my experiance is a hit or miss situation. As most of them are only there to complete their 2 year manditory regional school stint, before they can be accepted in a City posts. A lot are a total pain mainly because they are inexperianced holding a  degree in english, which they believe makes them all knowing in theatre & drama.- Big fish in a little pond syndrome. But they are enthusiastic enough & bring in new ideas, thus can't be faulted for that, the fact they have no idea is not important - they give it a go?
This is probably why groups in  Bush towns, have a policy of new directors must do a One Act play before being allowed to direct a full blown production. Which back fires when full fledged & experianced directors who choose to retire to these towns, give it away as a joke & the group looses them altogether. Also it tends to protect those in the groups purple circle, who have been doing it for far too long, they are growing & cultivating cobwebs. 
But with only about 1 million to populated the state beyond the Perth metro area - that's life!

I've worked with several theaters in a tri-state area, and all chose directors differently.  And a few changed how they did this over the years.   Most paid directors even when they didn't pay other staff.  A few paid technical staff, but not actors. 

I can see the problem when the group has the need to keep thier own house out of the dark. Unlike  those who use hired venues.
But it seems to me to be an American thingy to pay Directors & what have you, as it does not seem the case in the UK or here as a rule.
I doubt the standard of shows is any better or even worse, across the board. So it may be there is a bigger pool of pro's looking to coin a few bob, then is likely to be here. Thus these bods created thier own niche market in community theatre there?
This is also the same with hiring sets & lighting to do shows. I know a lot of pohmy groups depend on complete show specific set & light hiring, rather than doing thier own thing. Which may be also the case there as well. Of course the availability of heaps of hiring companies helps. Which ain't the case here, as the few only seems to exist thru hiring odd pieces of set, props & lighting gear.
So our markets seem quite different in a lot of respects.
Also it maybe we are too lay back & tend to use our own in house resources - In a she'll be right mate attitude! Resorting to the old beg, borrow & half'inch of the convict ancestors, rather than pay out to hire in.
Although inter group resource swapping has always worked well. Mainly because we are such a small theatre scene & some what remote to the main stream in the Eastern States.
Also I found when I was working over there for a while, there was a large ballet barre between the bods in  Pro & Ameatres, which has never been the case here.
I like Vickifranks idea of touting the local media Directors or even TV Add Directors, to fill your pool. [they might enjoy the chance to clean out & clhorinate?]