Hiya,
I'm thinking a couple of things...
One of the reasons your LO might not be interested in feeding anymore than 4 minutes could be the 2 hourly feeding. He might be snacking, so he's not too hungry for the next feed, therefore takes only a little, which means he can't last anymore than 2hrs and so on.
PP is right about your supply dropping due to lack of stimulation, so the other thing I'm thinking here is that you're probably also getting A LOT of foremilk when you start feeding from the other breast that is fuller, , are you? (I remember with both mine if I missed a feed and pumped I would get a lot of 'watery' milk).
Remember that you feeling your breasts full doesn't mean you necessarily have more milk for your LO.
What I would probably suggest you do is a double approach: try to extend the feeds and move to feeding from both breasts (single sided).
You feed from let's say the right breast, burp, offer same breast again (if he doesn't take it that's ok). The next feed you extend by 5 or 10min, whichever your LO can cope without getting distressed, then you feed from the left breast, burp, offer same breast again. And so on...
What do you think? Could it work?
xxx