This is the first suggestion that makes any sense to me as to the runner. If he went in the park and back out 41 secs later, that would seem to be a logical time frame to run into restroom, quickly use it and run back out to continue on his way along 10th. The other couple theories would seem a long time if dog located 50 ft from gate. Say he ran in, saw dog, ran immediately back out… seems like that would have taken less than 10 secs. And further might explain why he really didn’t have opportunity to see much since it’s likely he wouldn’t hear much inside the bathroom.
Also, Katie’s wife stated it was likely that Katie came into the park they 12th st entrance headed toward 10th st entrance to loop back home. So, she leaves Henry’s, walks across crosswalk at 12:09, takes left on piedmont, arrives at 12th street entrance, and walks through park to Charles Allen gate (which would total about 0.6 miles starting from 10 st. crosswalk at 12:09). There are a couple routes she could have taken once in park but this is most direct route to Charles Allen going main path loop. Assuming an average 15-20 minute mile, that would have taken her somewhere in the range of 9-12 minutes from crosswalk to the area her body was found around 12:18-12:21.
This path actually makes things more confusing in a sense because why was dog found 100 ft further than her towards the Charles Allen gate? Could the killer have been hiding in restroom, coming out and surprising both she and dog and dog immediately attacks, she begins running possibly towards park tavern (located at 10th and Monroe) thinking there’s guaranteed to be other people/ help in the bar/restaurant and open field /walkway would be most visible if others were around to help or see her? And perhaps he finished attacking dog, chased and caught up with her at that point?
obviously, this is all speculative but have lived by and frequented this park for 17 years and the more I’ve thought about it, the more it makes sense she went the loop of 12th to end at 10th/Charles Allen rather than going into and out of the same charles Allen gate.