If you google on it you'll find scripts for random selection -- create a script in DVDA to match and test. Expect some initial glitches -- IOW be prepared to tweak the scripting a bit to get it working well.

That said, the hard part I'd imagine is using the next & prev buttons on the remote -- the prev button works differently depending on the player, & sometimes not at all. If you want consistent playback I think you might have to go to menu buttons or BOV. If you opted for using the prev/next buttons anyway, I'd suggest to try and make using the prev button optional, where the viewer could still navigate OK if they only can use the next button, and use chapters rather than separate titles or menu pages as that's the one place the next button seems to always work.

And if you're planning on PC-only viewing, you might check out the software that's available for creating 360 degree views instead of relying on DVDs. This is the sort of thing you might see on on-line catalog pages, with real estate, &/or hotels. I think Quicktime VR started it, but several companies like Ulead came out with their own products; I have no idea what's available today.