Transferring sync by restoring a backup onto a new computer works pretty well. That's a new option only available since the latest update so I haven't had a lot of experience with it, but I've tried it a couple times on small test trees and haven't experienced any problems.
As far as parents missing on FTM that appear OK in Ancestry, that's most likely a preferred parent issue. Sometimes (who knows why) a parent won't get flagged as "Preferred" in FTM, so even though they're there, they don't show in the tree.
for how to resolve that issue.