Well this really isn’t an US versus THEM at all, it is just to point out that there are various and very different kinds of peony groups possible. The group I have been describing is basically that of gardeners who volunteer their time and effort. Generally gardeners do not grow peonies for any commercial goal - cut flowers, garden plants, retail, wholesale etc. I only point out that each kind of group has a different goal. 

Gardeners generally want to meet and interact with peonies during the bloom season and during the sale/planting time. Commercial growers are most busy during these times and unable to get actively involved especially if numerous planning meetings are needed. Gardeners want peonies with a wide range of characters and garden qualities, while a cut flower grower may have only a limited range of cultivars and have more concern with commercial aspects. 

A club that is composed of commercial members will be smaller than a club of gardeners simply because there are more gardeners than the there are growers that supply them with plants. Growers and gardeners certainly work together, but each of their needs are probably best met by an organization suited to their specific needs. 

For example: Gardeners can plan and schedule a bus tour, take reservations, arrange for refreshments, reserve a bus etc on their time, but when they visit a commercial garden, that garden gets a target audience of possible customers with very little effort beside opening the gate and setting up a few conveniences. Of course this is a simplification. 

Another: A commercial grower can contribute a supply of catalogs and price lists to a public event sponsored and planned by gardeners. Again they get a target audience of potential customers. 

On the other hand: Growers will want to meet in the off-season when they can get away without interfering with growing or marketing. Because there are relatively fewer of them, some may have to travel a greater distance perhaps stay overnight etc. This will not attract a lot of gardeners. 

My recommendation is ‘Know thyself’. Are you more interested in commercial concerns or gardening and landscapes?  Is your need that of large scale agriculture, marketing, advertising, packing etc. or what new hybrids are best for your garden?  Are you interested in cutting 200,000 stems for wholesale interstate shipment or do you want to cut some flowers of a special shade of color for your dining room arrangement?

The kind of organization that you form will depend on the needs of your audience. Plan ahead.