RAW converters certainly make a difference. Having read a few converter comparisons over the years, I do recall DPP doing better in some pixel-peeping cases than ACR/LR. It makes sense - after all, who knows the sensor better than Canon?
That said, I think that Lightroom's noise reduction is quite good. You have to play with the settings to get a feel for them, but it's great to be able to control for color and luminosity noise separately, as well as mask sharpening to prevent sharpening the noise.
The order of operations (boosting exposure vs. noise reduction) doesn't matter in Lightroom. If you reduce noise before you boost exposure, you'll probably have to reduce noise again after, since you will have revealed noise that you couldn't see before. I usually do noise reduction as one of the last steps, unless the noise is so great that it really bothers me. That way, I can make all the adjustments, see how much they've affected the noise, and then reduce noise appropriately.
Also, if I may ask, what was the subject that required exposing -2EV and then pushing it? That just seems like a recipe for noise...
Hope that helps.