Full clutch disengagement befire shifting?

First off, that grinding sound isn't the gears grinding together. Every gear in the transmission is all ready meshed together, no matter what gear you are in. It's just a matter of the collar meshing it's teeth with the appropriate gear. Just in case you wanted to know =)

Anyway, if you really want to have less time on the pedal, don't lift your foot off the gas. It's not something you want to try till you can really get your shifts down. The 1-2 shift is an easy one to power shift, so practice on that first. The 2-3 is a little longer and harder to do.