Assuming your original username was descriptive and not aspirational (!), OP, I think one of your problems is the cost of living in your area. I'm green with envy at some of the prices being quoted. (I'm in the SE.) Anyone saying you're paying out the cost of a mortgage on activities is definitely not in your neck of the woods!
For comparison, I pay (averaged out to include annual costs): £70pcm for DS1, who plays one instrument and one sport, £116pcm for DS3 for one instrument, two sports and one after school club (also does one free club). And £155pcm for DS2 for three instruments and one sport at county level (also does two free clubs). (DS1 and 2 are teenagers, DS3 is in primary.) I haven't included travel costs in this, but my safety valve for keeping those in check is the fact that I bloody hate driving them all over the place and refuse to do more than strictly necessary! I also haven't included exam fees, as they're too sporadic.
DS2 is probably the closest one to being overscheduled, but he loves it all and is a super-relaxed, laid-back child. He loves the social side of what he does as well as working hard at it. No one is pushed to do anything the don't want to, and there are various activities that have gone by the wayside after being tried out for a while. They all have lots of downtime, muddling about, playing on computers, watching the telly, and we spend lots of unstructured time together as a family.
You don't sound as though you are a pushy parent, OP, and your DD seems to have plenty of downtime too, so if you can afford it I would say, why not? It's lovely to let your DCs find their talents and be able to take their opportunities. I was offered a golden opportunity at 11 to train at a national centre of excellence in a sport I was talented in, but couldn't because we couldn't afford it. While that wasn't unreasonable, I've always felt sad about it and wondered what might have happened if my parents had found the money somehow. If you were to axe anything, though, I think I'd go for the drama stuff, which seems disproportionately expensive and is less special somehow, in that lots of kids do it - unlike the diving and gymnastics, which takes ability and talent and are your DD's favourites, it seems.