While parking is a great technique for most patterns there are some where it just isn't as applicable. The pattern I'm stitching at the moment is huge with lots of minute changes in color. When I considered how it would be to sew using parking, not only would I have to have 30-50 some threads going at any one time, but the waste of thread would be extreme as there was often a lot of space between stitches. It was just easier to follow colors one at the time and go where they were going, which believe me was in no way straight up and down.
I love parking, I've only started doing it but it's very easy if you always remember to have the thread in the starting leg of the stitch. Also, I tend to finger comb the strands whenever I pull a strand out to work. I have my threads in hair clips (the cheap bendy kind) and I just clip them out of the way when I work.
I use parking on my HAED designs too - I found it difficult at first but now I wouldn't use anything else. There are some great videos on You Tube on how to park. That's how I learnt. I love watching Floss Tube on YouTube which is basically lots of stitchers posting about their work, what they've bought, advice on stands and different threads/techniques etc. You really can learn a lot and it's fun to watch too :D
I admit you have to get used to parking, but when you're used to it, it's great! Work from the top of your project (left or right top corner) down, so the threads will hang at the bottom. If there are a lot of threads you can use a hairpin to keep them together and not create a mess with knots.