Conversion speed relies on speed of your computer, mostly the cpu. Anything that runs significantly faster on your machine (like WinAVI) is cutting corners and losing quality, or just basically screwing up.
It helps to have two separate hard drives...two physical drives, not just partitions on one. Have one drive as the target, the other as the source.
If you want to try it, FAVC is one option for faster encodes. It is free to download and use. You'll need AviSynth and Net 2.0 installed first if you don't already have them, but they are free and there are links to both at the FAVC site. Normally I advise using the HC encoder that is included since it produces higher quality, but if you want faster encoding times, use Quenc and the optimized preset for speed. You can find FAVC here: http://favcfavc.googlepages.com/
Whether the end result will be acceptable to you, well, you'll just have to try it and see.