I haven't grown or eaten those two particular fruits, but I've made lots of mixed preserves and I say, "Go for it!"
One possible way to get the fruit off of the pits (is that only the Nanking cherries that'll be a problem for?) is to wash them, crush them lightly between two plates if necessary to get some juice out, and then gently simmer them (in their own juice if possible) until they are very soft. Then either try pushing it through a food mill such as a mouli mill or a foley mill, or cool it and go in with your hands and try to pull the seeds out.
Two of my favorites have been:
"Black preserves": I simmered seedy tasty black grapes till soft, then ran through the food mill. The result was gorgeous black juice. I don't care for sugary jelly, so I thickened it with dried black mulberries, and canned it. The mulberries were sweet
enough it didn't need any sugar at all. Yum! And gorgeous dark purple.
Mixed preserves with tropical flavor:
Three equal parts by weight:
--- Tart apricots or plums
--- banana
--- Diced
apple or pear
A little bit to taste:
-- lemon juice
-- sugar.
Some batches I've added ginger or vanilla, sometimes not. Great either way.
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