Update:

The pulp from juicing peaches or nectarines is great to use for fruit butter.  I don't juice it till completely dry so the fruit's still moist and definitely flavorful.  I fill the steam basket absolutely full of washed nectarines that I've run a knife around the middle to split the skin. (Seems to help the fruit release its juice quicker. YMMV) Then steam till I have about 2 quarts of juice.  If I steam till the fruit is dry it seems to yield closer to 3 or 3-1/2 quarts of juice.

Then I run the pulp through a chinoise and add sugar to the sieved pulp.  For nectarine butter I'm going with 1 cup of sugar for every 2 cups of pulp but it's a personal preference as to how sweet you want it.  Then heat and process in BWB like regular.

The nectarine pulp also makes an excellent nectarine mustard.  I use my regular recipe for the mustard but don't have to use any thickener nor have any need to cook the mustard to thicken — other than bringing it to a simmer in order to jar and process in BWB, that is.  I did the same thing with the sieved plum pulp required in a recipe I make for dipping sauce — I juiced the plums till they were partly dry and then used the sieved pulp in the amounts required for recipe.  Again, no need to cook down to thicken the sauce as directed in the recipe.  Just cook to get to temp and combine flavors.  Less risk of burning a sauce or giving it that "over-cooked" flavor that happens occasionally.

Taking out some, but not all of the juice seems to let me have the best of both worlds and so far I've not noticed any loss in flavor.