Love the videos. Also, NICE laptop collection!
My own cap removal methods have evolved over the years from having no guidance and struggling with a single crappy soldering iron, to using the twist off method, using two GOOD irons, using hot air, then finally setting on hot tweezers as my personal favorite tool for the job. If cap goo has already started to rot your traces and the board you're working on is in very fragile condition the twist off method can still pull pads off the board even if you are extremely careful.
If you only have one soldering iron - the absolute safest way I found was to destroy the caps by cutting them off the board with a pair of side cutters then desolder the individual leads. I haven't seen anyone propose that method (at least not recently) so I thought I'd share.