I dont do the parking method. I find that first off, the threads get tangled in your working thread. No, I dont think it helps go faster. In fact, just the opposite because you have to keep watching you dont get the threads tangled or caught up in your stitches.
Ive cross-stitched with only needle for years. Recently I bought around hundred new needles and discovered that many needles with many threads allow me to cross-stitch faster.
Also I tried the parking method. It came horrible because of really close threads colors! And because I used a kit, the threads run out before I finished it. And the manufacturer asked me to send them a photo of back side of the cross-stitch to prove that the threads run out not because of the parking method :@ So never ever again!