What you need is scripting, which Encore does not provide.
I would play with putting each video on its own timeline. Use multiple menus to branch. Use 4:3 menus even if the videos are 16:9, so you can get more buttons on a screen. You cou ld try making them black so they might not jar with the different aspect ratio of the videos. Use very short transitions and/or motion on the menus to make the menu appearance less disruptive. (Trade off with number of menus re the 1 gig limit for menus.)
For many of the videos, you are now 2 clicks away: click one "menu" (the menu option that will take you to the previous menu), then use the remotge control numbers to select the next track.
When submenu 1 is exhausted, you go back to main menu (title menu), and select submenu 2.
Yes, the operator must know what they are doing.