Apologies for being two years too late, but I just saw your question when searching for pages with both "satsuma" and "cranberry".
Orange juice has some sugar in it, so I'd use a bit less. I just tried some with yard satsumas, in these proportions:
1 1/3 c satsuma juice (because that's what I happened to squeeze)
3/4 c demarara sugar (a brown crystallized, rather than moist and packable sugar)
12 oz cranberries
1 T plus 1 t grated ginger
a bit of unflavored gelatin
Boil juice. Add cranberries. Bring back to boil. Turn heat down to simmer. Stir in 1T ginger (which was what was at the end of a jar).. Cook about 10 minutes, stirring occasionally. Decide it's not thick enough. Turn up heat just a tad, stirring about every 2 minutes, for another 8 to 10 minutes.
That's when I decided the sauce wasn't going to get thick enough, and added a bit of gelatin. I didn't measure it, but probably used about 1/4 to 1/3 of a packet of unflavored gelatin. I had just enough juice to cover the bottom of th emeasuring cup. I added gelatin until it stopped going translucent, then added a bit - maybe 2T of the hot sauce, so the little pile on top of the rest would also get wet (and because adding hot stuff helps gelatin dissolve enough to swell).
Chill for a couple hours. Or, put it in the freezer for about 30 minutes, then the fridge.
Next time I may try just a cup of juice.