I don't know if you can manage this with your other kids, but maybe you could hit the hay with your baby and a pile of good books. Read a little, snooze a little, breastfeed a lot... that worked really well for me. 6 weeks is a little young for your baby to feed easily in the side-lying position, but maybe since you are already experienced at bf'ing it won't be as hard for you. Learning the side-lying position was a life-saver for me!
Either that or, as the other posters, said, learn how to nurse with your baby in a sling. Do you have someone who could help you? I *just* figured out how to nurse with my ds in the sling when he was 11 months old! Don't wait that long!
It sounded like you are actually doing great and just needed a little support. I completely know where you're coming from with the amazement at the constant
breastfeeding. I was prepared to do it frequently, but I had no idea what frequently meant. The books (even good ones!) all make it sound like 8-12 times a day is enough. Well, apparently your baby & mine haven't read those books! Take care & keep posting -- it's nice to get some good vibes once in awhile, eh?