Two responses come to mind:
If you are playing on a physical board, and with people who are willing, simply pre-determine the order. (Yeah, I don't like this idea either, but it is a way to mitigate the random factor).
Otherwise, it's a value calculation. The value of a decision based on chance is equal to the value of the desired outcome times the chance of the desired outcome minus the value of what you had to give up to get it.
The value of the desired outcome is 1 more action in the next turn. (This assumes if you don't bet that it will come up a particular round you'll get it the next turn - could have greater value if not getting it now means you're unable to get it exactly when you want it later)
The chance of a particular action appearing on the first round of a stage is very straight forward - 1/4 for the 1st stage, 1/3 for the 2nd stage, 1/2 for the rest.
The cost (that is, the value of what you give up to get it) is hardest to figure. There are two types costs:
1) The costs of being able to support an additional person (food, room if needed). However, at least for person #3, it's a safe bet you'll do it sooner or later, so the only real cost is action order IE if you're expanding you're house you can't use those turns to plow and sow.
2) The costs of making sure you're able to cash in (IE taking starting player). Given that it takes a turn to take starting player, and there's only a 1/3 chance that it will come up, it's a losing proposition. But if there's a big pile of food there, it might be worth it. (if food gained > 2/3 of a turn, go for it)
To know if you should be prepared in case FG flips on turn 5, ask if the following is positive or negative: (Note, I'm slightly misusing the term marginal here. Sorry to any econ majors)
V = Value: marginal Value of doing FG on turn 5 (That is, how much more valuable is it to have FG on turn 5 vs. turn 6)
F = Flip: likelihood of FG being Flipped on turn 5. (This is equal to 1/3)
C = Cost: marginal Cost (including opportunity cost) of being prepared if it is flipped on turn 5 (That is, what is the value of the choices you can't make because of your preparations)
P = value: independent value of Preparation (that is, what is the value of these preparations if FG is NOT flipped on turn 5)
What you said (in your comment) about getting a better return on a family member the sooner you get them is right on. But, it's important to differentiate between marginal and absolute value.
Absolute value vs marginal value:
The absolute value of using FG on turn 5 is: 3VP + 9 additional turns (which is a 32% increase*).
The marginal value of using FG on turn 5 is: 1 addition turn (~3% increase*).
*(these are compared to the base 28 turns. Obviously, you'll use FG more than once, and thus have more than that, but it is still useful for comparison)
You use the absolute value in determining if you want to do FG at all, but you use the marginal value to determine if I should do it right now.
Note about P in the equation: this represents the value of already having the room (and food) for an additional person. If you are prepared for FG on turn 5, and it doesn't flip, the opportunity cost of preparing for it to be flipped on turn 6 is 0! In a sense, P is the opposite of the opportunity cost of preparing for FG on turn 6 or 7 times the relative likelihoods of it flipped on those turns.
This is not an answer per say, but more of a framework for finding the answer. I've only played Agricola 4 times, so I don't have a feel for the relative values of V, C and P. By making sure you're ready for FG on turn 5 or by preventing your opponent from being ready, you're saying that VF+P(1-F) is greater than C, that is you gain more by doing that than you could gain by doing something else.