another
Dont know if my ideas will help, but having been in a very similar situation to you some years ago, as a single parent with 3 children at 3 different schools (DS1 walked to secondary, but I needed to take DD to her secondary, and DS2 to primary), plus the necessity to get into work by 9.15am 7 miles away (which meant that a long walk to primary school simply wasn't an option because that would make me late back to my car, and late for work), like sooo many others I really understand the often frustrating and tricky business of getting everyone to the right place at the right time.
Regarding your 12 year old: like yours, DD didn't have any secondary school friends who lived close to us, and she was physically small; she was mugged walking home by herself in year 7 which made her frightened to walk alone, plus after this neither of us were comfortable with her walking about 2 miles alone to school.
We resolved this by dropping her at around 8 at the house of a schoolfriend; they then left the friend's house together to walk around 2 miles to school from the friend's house - so my DD's walk was about the same distance as if she'd left from our house, but they kept each other company/safety in pairs. This arrangement worked successfully for many years, and gradually over time they 'collected' other friends along the way, and the group walked together. It became a very friendly journey, and she is still friends with these girls (she is now in her mid 20's).
Could this type of arrangement work for your 12 year old?
This gave me plenty of time to find a parking place near-ish DS2's primary school. We always parked in a quiet road a short walk from the school, maybe 5 or 10 minutes away and not right up by the school; would wait in the car until it was time to walk in - had a hot chocolate from a flask, read a book, sing songs etc; I then had time after drop off to return to my car, and drive to work in time. Once we were out and about in the mornings everything felt leisurely and unrushed, and those times in the car with my youngest have become very precious memories.
Would also suggest speaking to the head of your primary school about your ideas regarding a drop-and-drive arrangement for older children, and become proactive in trying to tackle the parking/dropping off issues at this school: develop a positive diaologue with the head; join PTA/Governers etc. Lots of other posters have offered some great advice.
Some people dropping kids off by car are shocking in their selfishness and sense of entitlement, and there's really not much you can do about that, but trying to pursue new solutions sounds far more satisfying than the current struggle you, and probably many other parents, try to deal with during this hectic drop off period.
Hope you can find positive solutions.