Just to let you know: the two 4GB sticks are stable even under max-stress BurnTest. Furthermore, because I was curious, I shoved my original two 2GB sticks in the other slots and tested again. Guess what? Stable again. Presumably v2.12 of the 2GB stick is dodgy in some configurations; the original set I bought over a year ago is v2.2 (no idea why the "new" set is actually outdated, but they're returned anyway).
I think I'm still going to see if I can grab a bargain on a decent board, 'cause it seems a waste to not overclock the i3-540 (seen evidence it can hit 4.5GHz even on the stock cooler - it's at 3.06 currently!). I've got my eye on a Gigabyte P55-UD5 at the moment...
Thanks once again for all your help!