Here's a thought. Rather than doing curls, wouldn't you be addressing your biceps ~fairly similarly with horizontal rows using, say, a supinated grip? In this way, you'd also be working areas of your back that don't get addressed as much when doing pull-ups.My biceps are something that need just that little bit of attention and are easily isolated with 3 sets of barbell curls once a week. Nothing major there.
If I do squats, dips, push-up variations, overhead barbell press, pull-ups, upright rows ( yep, I know the supposed dangers ) I’ve got my MY requirements covered.