I think that's the right idea, but it appears to be the other way around: an -e for existence, and no suffix for motion. Good catch. I missed the Tips & Notes section on my way through here the first time, where it says all this. I'll assume that's how it goes: -e for fixed location, - for movement.
Other points of interest addressed at no one in particular, because apparently I have nothing better to do right now:
Throwing the two different sentences (on, onto) at Google Translate yields the same answer, but I'm not considering that to be an authority on the language.
In Tips & Notes, the Direction and Motion table doesn't have "to" for any of the motion entries, but I think that just might be how the table is, and the "to" is implied. Just something weird I noticed. "X goes on Y" means that X belongs there, not that X is going onto Y.
Just to clarify the above with actual examples, can someone confirm that these sentences and their respective English translations are correct?
Han hopper opp på bordet = he jumps on the table (i.e., he is already on the table, and he is jumping up and down there);
Han hopper oppe på bordet = he jumps up onto the table.
I'm pretty sure that's what the above discussion is saying; I'd just like to be sure. Tusen takk!