Normally a summoner can ride their eidolon as long as the size difference is at least one class. That allows them to fill the same space(s) as the eidolon typically. Small or smaller summoners then able to fit in a normal medium space. They don't spend an action moving in that case as their eidolon uses their action for movement. However, the summoner has to spend one of their actions to control their eidolon. Basically you end up with 2 actions each and one action taken by the "mount" is typically a stride action. I believe in this instance the concept was that Cynthia was effectively an eidolon mount in this case.
Edit: If there are "tandem" feats in play that's where things can get complicated for Summoners, heh.
I used a ruler for my line, and it should technically avoid Krot although diagonals are strange in a square grid, lol. I figured the crossover point was further based on the line, avoiding Krot. Regardless, I didn't realize that Sal was there. Thus its an issue.
Your solution works, I'll edit it. The one difference being that she can move across the top with a single move, launch the boomerang from F9, and then use her half stride (from the impulse gate) to move after the impulse back 10' away from the doorway to H9. That leaves the entryway clear for the others and still hits the two trolls safely. :)