Have you tried to get a sling? He may not stay in it for a long time (mine did not like for more than 30 mins) but it frees your hands to do a bit of housework - I can put away laundry, water plants with ds in there.
Some women can even bf their babies in there! I never made that work though.
Once you have shushed ds to sleep, can you slowly lower him into a buggy and if he starts to stir, rock and push him around until he goes back to sleep. I found that if I put my ds in a buggy after I had nursed him to sleep or whichever method you use, I could get him to sleep longer. Basically babies go through cycles of shallow and deep sleep about right. If your ds is coming out of deep sleep (20 mins sounds about right), he might wake during the shallow section. So if your ds is in the buggy, you can rock him when you hear him stirring to get him through that shallow section into the next deep cycle (maybe 10 mins). This way, I could get 2-3 hours of nap if necessary. Even if you had to rock him to keep him asleep, there are things you can do one-handed, like read the papers/mail, a bit of cleaning, writing lists, planning menus etc
Check out the mechanical swing as well. It worked for my dd for a while, but not as successful with ds.
And I echo what others say about it getting better once your ds gets older. With every milestone, like sitting up, crawling, walking, your ds will get better at amusing himself.
Hey, I've got 2 babies like this (dd is now 3.10, though ds is only 10 months), so I know what I am talking about.
Don't worry about bf-ing being the cause. It is not. Some babies are just like that. That is why you did not get it with your 12 and 7 year old. You know, gr8kids, chances are, your ds is going to turn into a sociable, lively and very engaging little fella. His personality will start to shine through more and more. Looking at my dd now, I can see why she was the way she was as a baby.
You are one lucky mother! This phase will pass.