I agree with Texas Stitcher as far as weaving it through the back of the stitching. If it was me, I never park the needles. I did that before and you end up paying more attention to the parked needles (not getting them tangled up with the needle you are now using) than actually stitching. You could have different needles with different colors on it in a pin cushion (I use paper with the color # on it and park my needles with the corresponding thread on it instead). I hate parking, it's confusing, especially trying to remember which needle has what color of thread (most is so alike in colors).
Just do one color at a time for a perfect picture and less stress. You have all the time in the world to finish (if not, then you will have a more prettier picture when complete) if you use on color at a time.
Make a copy of your pattern and mark the color(s) you have completed. You can do sections of one color, mark it as complete, then go back with another color and mark complete, etc. I do all my stitching in sections (sometimes 100 blocks at a time when I use Aida). Or sometimes if it's multiple pages, then I do one page at a time. Hope this helps. Sorry for the lengthy message.