I think the best speed run strat will be using the 10 run mercy rule, which kicks in at the bottom/end of an inning. If you are 10 runs up (or down) at the bottom/end of inning, it triggers the "Game End" sequence.

The question then is do you bat first (Bears) or pitch first (Eagles)?

The mercy rule kicks in once you are 10 runs up. So if you bat first you can rack up 10 runs, change over, and then get three outs on the Eagles to trigger the rule. However if pitch first and bat at the bottom of the inning, the mercy rule kicks in at the 10th run without having to finish out the inning.

When working on strategies it's tempting to bat first. The pitches and types hits are very random driven events, so by batting first you can better control the random event generation with accurate timing. Of course by the time you get deep into the top of the inning (batter 5 or 6) the vagaries start to get uncontrollable.

I feel that the better strat would be pitching first. You are still dealing with random driven events, but because you can move so much faster through the pitching sequence they are easier to control.

My PB right now for pitching at the top of the inning is 76 sec to the "change". This is based on three batters hitting infield pop balls on the first pitch that are easily caught. I can get this 76 sec about one out of every 20 to 25 times, I need to do more work on finding the best sequence.

In general though a "quick" three-up three-down pitching at top of the inning runs anywhere from 1:00 to 1:10. (Getting those long fowl balls is the death nail here because they can add 7 sec or more per event, and some sequences I've seen 4 long fowls)

Of course even with a top of the inning that runs long, what maters more is how you play the bottom.