It's always daytime if I'm headed to somewhere other than the Market. Whenever I try to go there, the bridge is certain to shut on me seconds before I reach it.

Secrets like that were what made Zelda OoT known as one of the greatest games of all time. Not only the larger Stalchild, but the larger Guay also existed; and so did the Purple Leeva.
The mini-game idea sounds cool. Imagine a larger Like Like, or Iron Knuckle. The Like Like could suck you up from a further distance, and the Iron Knuckle's axe would reach you from afar, making the battle fairly difficult.
I think that the Stalchildren did grow into Stalfos by natural means. Most monsters of the dead have some magic about them, but the Stalfos seem to rely on raw damage in battle. They prove worthy opponents, something that could only be achieved through experience and practise. The Stalchildren learn to fight at an early age, and although they're not very good at first, they have plenty of time in 7 years to get to the rank of the Stalfos.
This also explains why there were lots of Stalchildren, but a limited number of Stalfos. Some Stalchildren may not have had the skill to become a warrior.
I have a theory, that underneath the field, there is a whole new land, where the Stalpeople live. They seem to be able to dig up to the surface anywhere they want, so it would make sense.
Their land could also include the grottos, and the place where the ReDeads are underneath Kakariko Village.