While this isn't about improving the bigfoot, I kinda think now how they could have gone about of how sims could 'adopt' the bigfoot:
What If instead of getting a map to the bigfoot's whereabouts hut, your sim had to camp out in the woods (like witches/vampires, but waiting they days) where there been reports (following rumours, sort of like in eastern eggs) of sightings of the possible natural habit of the bigfoot. The Player would have to put all their attention in 'catching a bigfoot', because once the creature appears at the edge of the lot, 'It/he' will run to the other end of the portal to escape (or even better, bigfoot would have unique pattern of entering&leaving the lot: just by going through any corner/edge of the lot instead of going across the sidewalk). Not only that, the lot would need to be heavily build with dozen of trees (making it hard to spot the beast) but within a very small lot (to prevent immense lag, as well making it challenging to time the pause button or capturing the bigfoot). The Player would need to initiate any social interaction to disrupt the bigfoot fleeing interaction. Once the bigfoot is stopped, the player would need to sent a sim to greet him which the action, in turn, would have the bigfoot invite the sim over to the lot. Then the bigfoot will leave the lot, leaving the sim with the "membership" card/map to the hut. The Player will have no choice (unless (s)he doesn't restarting the process) but to visit (and no other community/home lot in between) the unlocked secret lot right away. Once the sim follows the bigfoot to his habitat, the player will have to make the vacationing sim befriend the Yeti only at that right lot (If there's still the motivate to move him the creature), because again leaving the lot will result in the loss of membership to the lot and the relationship between the sim and the yeti would reset (bigfoots don't have a telephone/computer, so there would be no means of contacting each other between the stranded and civilianize land).
Oh, I haven't realize how the part of "act-fast" resembles very close to catching a ninja to ask the technique of how to teleport. Still, it would be quite fun and challenging than the easier route of found the map - now I can visit and adopt a yeti at any point of time in my life).
P.S. Sorry for my bad english.