What makes you think he's not getting enough sleep? If he were really exhausted surely he'd be sleeping for long periods rather than waking. So it seems to me that either he's waking because he's hungry or because he doesn't need the same amount of sleep as some other babies you may have met. At 5 months it's textbook normal for babies to wake in the night, have a feed and go back to sleep. They're growing a prodigious rate at this stage. And some babies just need loads of sleep whereas others are more alert all the time.
We sort-of did attachment parenting-lite, for context. I don't think mine slept through the night without a feed till he was about 11 months or longer (same for non-attachment parenting friends I spoke to with theirs) but I didn't fret about it because we were co sleeping and he was breastfeeding, so there was virtually no disruption to my own sleep. From my recollection of this some 4 years ago, you're doing better than we did as my DS was still waking to feed about two or three times per night at 5ms.
Yes, your DS keeps waking, but it's not the attachment parenting that is waking him up. This won't go on forever, and weaning is just around the corner, so that will have an effect on the frequency with which he needs milk.
Re self-settling, I hate to be a bore, but the evidence that stopped me from sleep training was that that showed that the reasons sleep-trained babies make no noise when put down has nothing to do with being calm, as their heart rates show they are actually extremely stressed. But, yes, they do learn how to sleep without you earlier. In the general context, is delaying this useful talent a big problem? Sleep training has always seemed to me quite unnecessary for the child but a big boon for a parent who has to go to work, look after the child's siblings, wants free time in the evenings, etc., and I'm sure that's why it evolved, but there is nothing to show it makes for a happier more well-balanced better-behaved child. My DS is really confident, very independent and very happy, btw, and people often comment on it. I say this not to show off but to reassure you that you have not been ruining your child's life by any means.
I think with parenting you should do what you feel is the right thing to do, and ignore other people if you have a gut feeling. If you feel happier being cuddlier parents, stick with it or you'll just make yourselves miserable. If you think there's a need to get your own lives back, however, there are loads of books out there to help you sleep train nicely, but most I looked at suggest you don't start till he's 6ms as right now he still needs a lot of reassurance and your skin-to-skin contact.