If you are only trying to turn the spindles to realign them, you don't need to pull the spindles out. Just heat the head right around the spindle and it will turn when the head is hot enough. Unless the spindles have a lot of miles on them they are probably OK. I know everybody's inner anal expert wants to pull them out and check the condition though. Me included.
Pulling the spindles with the head on the barrels sucks, if that is what you are doing. Lots of things to consider and a lot more care is required. I don't do this every day like some of these guys do, so they may attack the task differently. I just happened to be doing it yesterday.
The spring washer and shim washer usually fall down around the spring cup if they fall out of place. They can be fished out with a small hook like tool. If they go down the pushrod tunnel, you'll be lucky to fish them out. Although that has never happened to me yet. Only done it about 10 times though. A hook tool can also be used to pull the spring washer out once the spindle is clear of the spring washer. I don't pull the spindle all the way out until I have control of the spring washer and it is out. I use a small pair of angled pliers used primarily for small electrical parts work to compress the spring when reinstalling it after getting the spindle almost all the way in through the rocker arm. I also use a small screw driver to move the spring if I screw up aligning it right off the bat during reinstall. The valve springs make using bigger tools difficult, so I use small tools.
BTW, I would imagine a lot of used bikes that have had several owners and have had head work done have spindles that are slightly out of alignment along with just about every other part on the bike. lol