Pesky punctuation

Is this what they call a 'teachable moment'?

The Young Writers don't want to be young.

Seashore Family Literacy has three writing groups — for ages 9 to 19 — and the teen writers have said they aren't all that young (compared to the nine-year-olds, I suppose this is true). Admittedly, I opened the door to this discussion, and they had a point.

The grade-school group is called the Happy Hour for Young Readers & Writers. The middle school group is the Writing Club. The teens, formerly the Young Writers, don't want to be confused for inexperienced, impressionable youth. After all, they are older and wiser than their younger colleagues. 'Young,' they say, is patronizing (until you are 40, I say, and swoon at anything pore-less and firm). They want to be the Writer's Group. Not teen writers, not young writers. They want the shorthand of Writer's Group. I get it.

But here's the rub: The pesky apostrophe vexes this choice.

Young Writers was easy. A collection of writers, no possession and no need for apostrophe. But how to punctuate Writers Group? Is it Writer's ? Writers' ? or Writers?

Begging of friends, pleas to teachers, and endless Google searches offer no relief. Where's the model? the rule? (I haven't been this muddled since the Farmer's Market debate of 2002 -- Farmers, Farmer's, or Farmers' ?). Instead of a clear answer, I find that I am in a room packed with equally befuddled writers.

For example, here's how others handle the apostrophe:
Pacific Northwest Writers Association
Writer's Market
Tallahassee Writers Association
The Kenyon Review Writers' Workshop
Tin House Summer Writers Workshop
The Alabama Writers' Conclave
Santa Barbara Writers Conference
Oregon Writers' Colony
Writer's Digest . . . . and on it goes

Clearly, I am not alone in this predicament. Can you solve this grammar dilemma? This could be your teachable moment, providing me — and a group of not-so-young writers — with great knowledge, comfort and relief.