I hate to say it but you may have to poison an egg plant and then plant a new one and stand by to make sure you are there when it produces. Hopefully someone with a Bog house will see this and help you.
During the beta, people used to post in Global Chat whenever they found an egg plant with one egg on it - maybe keep an eye in there. Although I haven't seen anyone post recently & I think you're probably right... it's cos the plants are being watered & petted too much.
I think one of the root causes is that players tend to consider where they first started in the game as "home" for a while. During the beta, new players only spawned in Groddle and so these areas were heavily populated (but not as heavily as now!) while the more distant areas (where more of the egg plants are) were less heavily populated and so you could usually find an unloved egg plant up in Kajuu or thereabouts. But now these more "distant" lands have new player spawn spots in them... it's quite weird to walk around, say, Alakol and find a street with 30 level 4 players on it.
As a result there's large numbers of people petting & watering egg plants in the furthest corners of the land. I think you're right... no fully grown public egg plant is ever going to be down to its last egg (unless we put together a quest with 20 people running around like a plague of locusts, stripping egg plants).
Another alternative might be to poison an egg plant, plant a new one and harvest its first egg. Gotta learn botany for that though & that's a lot of work.
Yeah, I've been having lots of trouble with this quest with the new flood of people. I've started to add into my routine a daily egg hunt, and though it provides a lot of energy I haven't been able to finish the quest.
Y'know it might just work. I wonder how many harvests a fully-grown egg plant can supply. We'd need at least that many people on the team. Plus we'd need an area with at least that many egg plants so that everybody could get their Last Egg Standing quest fulfilled.
Given that the words "cats" and "herding" are generally mentioned whenever anybody tries to organize joint gameplay, I think this is one idea that's likely to remain just a theory.