I have the same problem. Only my rims have over 12k on them now and are probably good for a few more. Thats why I'm making arrangements to pick up a new set soon so when they do go, I've got a new rim in place. This new set will be my fourth set of rims. The last set was a pair of Velocity Aeroheats which were supposed to be so tough and everything and they lasted a little over 8k. I went with Sun Rhyno lites to replace those. And they are as advertised. Good strong commuting rim. If you're only getting 6k or so out of your rims then you need to get better rims. You could switch to disc brakes but you'd need a new frame. They sell kits to modify your frame to accommodate disc brakes. You'd have to replace the fork for sure though.
Wearing out three chains in that time period isn't so unusual. I've worn out plenty of chains through the years. I use a Park chain measuring tool to measure the stretch. And when its time to go then I pop on a new one.