It's definitely doable but you'll probably need to frequently change the way you do it as puppies change so fast. That's my experience anyway.
I agree that you couldn't carry an 8 week old OES for an hour - think ours was 5k at that age but the week before we could put him down he was 8kilo and wriggling to get down! That week I did very few socialisation trips as his wriggling & weight were too much.
So I'd leave him at home for the hour with a kong till he's had his jabs. (Unless you could get someone to go with you on one or two school runs to share the carrying as you want him to get used to trains early on)
Once he's had jabs, I'd take him some days, leave other other days. Then you can pop into school sometimes if you need to and also get a break every now and then and taking our OES on school run is really intense. Ours is about an hour as well - 20 min walk each way, but bus one way at moment as he can't walk both ways yet. The hour is full on - they pull on the lead, they love greeting people and children so a lot of restraint involved and so many people want to talk about the breed that it's hard to juggle being polite, chatting and managing an excited puppy! You couldn't do it 10 times a week.
I take minty on the school run about 3 or 4 out of the 10 now as I've realised that suits me and he's fine being left - I fact I think he needs a break after being excited throughout the daily family breakfast so flops out an sleeps!
I put a new pic on my profile of minty at 14 weeks old!
Have you got anywhere with the breeders feathered? Took us about a year (and being on three breeders lists) to find minty.