As far as cooking goes, I do the same, I make jellies.
Initially, I used to pick each berry and tried to avoid picking the stems, but it's way too tedious . And as you mentioned, if making jellies, you run everything through a sieve anyway.
What I like about the red currants, is they have a natural pectin, so when making the jelly, it's basically 2 ingredients , currants and an equal weight of currants 1:1 ratio. You can cut back on the sugar a bit, but Im not sure where the actually line is oof cutting back too much, that may affect the consistency.
Another thing I do , when making jelly, is use currants as the base, but maybe use 2/3 currants and 1/3 another kind of berry ( like raspberry or blueberries). That raspberries work really nice, cause their flavor hijacks the currant flavor, and it basically becomes raspberry jelly. The blueberries get more overpowered by the currants though, but they give the jelly a nice dark color.
I've seen people garnish with currants, or toss them in grain-like salads ( taboule) and even cows cous dishes,
What surprises me the most is just how productive these plants are. I can, and have spend an hour picking the currants and then take a step back, and it looks like I didn't even make a dent.