I don't think there's a way to buy all non-electronics parts other than buying them all one-by-one, which doesn't seem to be a solution for you. Note that contacting the LEGO customer service may be an option, but I'm not sure how far they'll be willing to help (and as you said it probably won't be cheap).
The only other idea I can suggest is to work the opposite way: try to sell the electronic parts you still have; that way you can just buy a complete kit again.
I realize it's not really easy either, but there could be some people who have already so much regular LEGO parts that only electronics interest them, and they don't want to pay too much money by buying these separately. Or maybe someone has the kit and lost some of the electronic parts.
Of course, don't underestimate the use of having extra electronic parts - your robot can get much more interesting; and in particular, learning to program two different NXT bricks so that they communicate properly to achieve a common goal can be very educational. Also, considering a full kit is usually cheaper than buying all elements in there separately, I believe buying it again is a more interesting thing to do - although I understand the price can be a serious issue, especially if you want to buy the newer EV3 version.
There may be another thing you can try: as you probably know, LEGO has educational programs based on robotics kits, and it could be that a school/college in your area is using these. Try to contact them, and see if they would be willing to either sell you unused parts (maybe because they are upgrading to EV3) or to buy your electronic parts (if they lost or broke some). I'm not sure if you can contact LEGO Education to try to get a list of schools using mindstorms in your area, but it can't hurt to try.