I'll try to explain stage 2 now.
When I talk about the Ice Palace, I mean this part.
The big man's spawn is determined by how fast you go through the Ice Palace.
You want to get through the Ice Palace in the fastest way possible
that doesn't cause a bad spawn.
For example, here's what happened to me:
7115 spawn - 113 X-position - BAD spawn (unusable)
7118 spawn - 110 X-position - BAD spawn (unusable)
7121 spawn - 112 X-position - OK spawn (fastest usable spawn)
In other words, I had to intentionally waste 6 frames in the Ice Palace in order to get a spawn that works.
Why is it important to avoid a bad spawn? Because the three birds are on a timer, and the timer doesn't start until you get to the house.
If you get a bad spawn from the big guy, you can't jump across the water and start the bird timer. You have to kill the big guy before you can start the bird timer (a loss of a few seconds, thus unusable).
With the OK spawn, you can enter the house area and start the bird timer, so it doesn't matter that you have to fight the big guy before you can climb the first ladder. All that matters is that you meet the third bird at the exit to the house on time. About 336 frames pass between each bird's appearance no matter what.
The only remaining complications are (1) the birds show up slightly inconsistently (e.g. 335, 338, 339 frames) and (2) the speed of the third bird is somewhat variable as well. And so I am trying to optimize how soon the birds show up and how fast the third bird flies.