Well, I solved my problem, but in sort of an "illogical" way. Please read my earlier descriptions of the design of the activity. There is one error in the prior description--the Player train will fit on the yard track that its path enters at Lloydminster, fully clearing the main line that will be used by the AI trains. Apparently, the AI Dispatcher doesn't care about that, only that neither the westbound Player path or the eastbound AI path have any passing paths in order to make a meet. So, my "illogical" solution was to place Passing Paths on the Player train path at the two sidings long enough to fit the Player train between North Battleford and Lloydminster--the sidings at Breslayer and Waseca--(according to the OR manual, such passing paths in the Player train path are usable by either the Player or AI train), knowing full well that the neither the Player train nor the AI train(s) would ever meet at either location. When I ran the activity, I was fearful that the sim would crash once the Player train passed the last passing path available (at Waseca) for a meet, but it did not. I ran the activity all the way to Lloydminster, switched the Player train into the yard tracks (using manual mode for this), then spotted the Player locomotives on the yard track included in the Player path, lined all switches back to the main track for the AI trains, then took the sim back to Auto mode. The "parade" of eastbound AI trains behaved just as they should, continuing to run their full path to North Battleford. Please note that Location-linked Passing Path Processing was checked when I ran the activity.
Designing an activity on an unsignaled route is indeed a challenge if one plans to have meets on the line, but I did figure out how to accomplish it in this case. I should note here that Blackfoot 3 is, without doubt, one of the best routes in MSTS/OR. Beautiful detail, lots of main line and switching opportunities, and realistic operating possibilities. It is also VERY true to the prototype, including, most importantly, that it is unsignaled. If you haven't downloaded Blackfoot3, installed it, and run it, you're missing out on a real treat.