I've done this sort of move before with removalists. Bought a cling wrap thing from a stationary store. Don't know what they're called, but basically a small roll of cling wrap with a handle for packing stuff. Then just quickly wrapped each draw in both directions. It's fast, cheap and 100% effective. Just remove the wrap at the other end.
Yes, I have used this method as well. It should be OK, as long as you keep the cabinets upright. I also put a small bit of crumpled up newspaper in each drawer to stop the parts from rattling around.
To anyone: do yourself a favour and don't buy these kind of 'component collections'. The reason they got left over is because they had no use. It will just take space and when you finally throw them out you still feel sorry for wasting money. Been there, done that
I would agree with this to a certain extent. It is not worth paying real money for such a collection IMO. But if you can get it for cheap, and have the space to store it, then it is probably worthwhile. Even if most of the parts are not common ones, it could be the difference between getting inspiration for a project and implementing it right away, and having to wait a couple of weeks for parts to come in, by which time you might have forgotten all about it.