That tree sounds beautiful! You can do a lot with those mulberries! You can preserve them:
To preserve Mulberries whole.
Set some mulberries over the fire in a skillet or preserving pan; draw from them a pint of juice when it is strained; then take three pounds of sugar beaten very fine, wet the sugar with the pint of juice, boil up your sugar and skim it, put in two pounds of ripe mulberries, and let them stand in the sirrup till they are thoroughly warm, then set them on the fire, and let them boil very gently; do them but half enough, so put them by in the sirrup till next day, then boil them gently again, when the sirrup is pretty thin and will tard in round drops, when it is cold they are done enough, so put all into a gallipot for use.
Or you can bake with them. "Food Down Under" has some good recipes using mulberries:
Here's a fudge recipe, too! :)
1-1/2 cups ripe mulberries (to make 2/3 c Mulberry juice)
2 cups sugar
2 tablespoons butter
You can use this recipe for any low pectin fruit eg.
Saskatoons, blueberry, elderberry, raspberry, blackberry or May-apple.
Cook 1 1/2 cups of ripe mulberries[unripe fruit is toxic- see about Red mulberry], mash and drain through a fine sieve or jelly bag to obtain the juice: about 2/3 cup yield.
Mix juice with sugar and butter and cook over low heat until sugar dissolves.
Bring to a boil on medium and boil without stirring until soft-ball candy stage- 240 degrees.
Remove from heat; cool until lukewarm and beat with a wooden spoon until mixture looses its gloss.
Press into a buttered pan and cut into squares before the candy hardens.
Keep in a tightly covered dish or freeze because this candy hardens when exposed to the air.