by Ken Task.
Part 2 - once you have those site backups ...
Site restore ... only maybe not with MAMP ... VirualBox with a Linux distro CentOS 6 or Ubuntu vr? that one could use PHP 5.4 or .6 upon which to restore site.
Once on a VB server you control ... git side load to a 2.9.x ... upgrade site via git and cli scripts in code/admin/cli/. Check site with browser ... backup code/DB ... upgrade via git + scripts to 3.0.highest .... ditto. Once a 3.0.x, one could try a course backup from the VB site and restore to true server.
Fingers crossed at that point.
'SoS', Ken