Lots of good advice above; practice for precision first and add speed later, revoice or refinger chords to make things easy on your self, and judicious capo application are all worthwhile when working up difficult new pieces.

When you mention "Mixed Picking" remember that not all fingers may not need to reach the new chord simultaneously. Learning to fret strings for only the precise time needed can be the hardest part of making the strumming to picking transition. Find some videos of good players (try Bela Fleck) and watch for the subtleties of which fingers press first, even when they are strumming chords.

Good Luck!