OK, I think the actual problems i was experiencing with pasting the automation might have been user error, or might have been logic behaving strangely, whether it was because I was loading files from a new version into an older version, or something else. But now everything seems to be working fine for me. Thanks for the all of the replies, I know there were some others on here that were also experiencing this, so maybe there's still something to glean from it.
Also, another part of the question was, is there any way to take a whole part of the timeline, copy all automation lanes from all tracks, and paste that in a different part of the timeline?