Pick out what you really, really, really want. Set it aside. It is not for consideration for the rest of the plans.
Surely you have a couple cousins, and the cousins have children, or even adult grandchildren? I would “gift” them with the stuff, but use a pick up date as 1ke suggested. Get their addresses or email from parents. The letter goes something like, “Dear Hortense, Great-Grandma always cared for your mother/ father, and knew she would also care for you. Although she never met you, as she tragically died before you were born (even if Great-Gradma would have been 125 when Hortense was born), I know you were meant to have her china (bedroom set/ shawl/ tin water glasses). While I have been the keeper of the family heirlooms, I no longer have the room to do so. So please- Come and pick up your china (bedroom set/ shawl/ tin water glasses) by July 5, 2008. I am at home on Saturday afternoons from 1:00-4:00 PM. I would hate to think you wanted them and didn’t get them. After July 5, I’m afraid I’ll have to dispose of them in some fashion. My best to your mother/ father/ children/ dog. Love, your cousin, KathyA.” Lay in a supply of light snacks and beverages, and prepare to have your kin come tromping through town on Saturday afternoons for a couple months.
When they come, after they’ve loaded up their stuff and you’ve had some conversation and light snacks (ignore any hints that they stay for supper), give them a small box of the already digitized photos and other memoribilia as a “surprise” for showing up. Even better- If they bring their kids, hand it to the kids! Be sure to place emphasis on their value, and how you know Grandma would want such lovely children to have them and treasure them.
Have your purse and car keys at the ready at 4 PM, to induce people to leave. Even if you just drive to McDonald’s or the store, GO WHEN THEY GO! You have an “urgent appointment” at 4:30, and you simply must dash!