If I transfer songs to a zip drive and reload, can I get them out of "Purchased"?
This is a bit of a grey area around fair use, but there is software out there that will allow you to remove the drm from iTunes songs. Given that the songs they currently sell do not have any drm, I think it's not a particularly immoral option.

If you want to stay on the clearly bright side of the law, burning the songs to a cd and then re-ripping them will remove the drm and is supported through iTunes. You will lose some quality though.