{+1 Karma Award to first person} Can anyone state the total number of possible FE New Game start possibilities? In other words, after a player sets all combinations of settings to their liking, how many players could have a unique set of settings when they start a game? {Do not factor in Customized Opponents – so total of 8 possible AI opponents (no teams/no AI custom difficulty).....
As a person that was rather good at math in my school I think you are rather vague, so I will have to give it a try
(Not a statician myself, but I do know how to press on and work on it until I die.... or its done
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I first list up all the different options, with how many possibilities that is present:
Hmm when I look at some of these items, it seems more difficult than imagined before... 
anyhoo: https://www.dropbox.com/s/ls00kcm2hiho1cn/Temp%20Ele.txt
Notice I also disregarded custom starting sovereign....
A thing I really need to know is how much "Empire vs Kingdom" balance is a factor, does it just change the random variable (in this case I would consider it important), or is it trying to acheive a certain number of empire for each kingdom faction (in this case I just got a headache...
)
So I take my first factor (starting sovereign) and mulitplies it with the next, and then multiplies that number with the next, to get the amount of different options.
The reason I do like this is: For each time I pick "Relias", there is all the different map sizes to pick between, and all the different map types to pick between.
I have left out your custom maps stamps... Because that would give me a headache
and I don't own the current map pack DLC.
Now I have a calculation that looks like this:
8*4*7*6*5*5*10*4*4*4*4*5*8*10*6*5 (this equals 1032192000000)
But I stopped at victory conditions, because they can each be modified individually, showing the state of either "On" or "Off", so I find out how many combinations of victory conditions are possible, so for each "on/off" switch I have the number 2, and times it up with 2, so 2^4 = 16
And we add a "*16" at the end to get the final line of math:
8*4*7*6*5*5*10*4*4*4*4*5*8*10*6*5*16 (This equals 16515072000000)
Now I as a gamer see's a problem with these few options, and that is I included some "Random" options, and some of them to me have less of an effect to the starting position, which is why I said you were "Vague", so to reduce the number above I would first off remove the random variables since they right now produce doubles, I go back and make a new count of each seperate item but exclude the random one.
and our big string of numbers is going to look like this:
8*4*6*5*4*4*9*3*3*3*3*4*8*9*5*4*16 (this equals 1031956070400)
But, you have seen my posts and know I am a critic at heart and some of these options I would exlude if I was major of testland.
How important is it really to start a game without ANY victory conditions?
How important is it to my game to decide upon the AI which miniscule chance they have to be empire/kingdom? is surrender threshold really all that important? now there are too many variable for me to list all the bloody numbers of what might give you just the right set of options, so I would rather give you the ability to do the extraction of any single item yourself.
We have our 2 lists of numbers, pick a result and do the following
If you want to eliminate the idea behind starting sovereign, divide the number by 8
If you want to eliminate the map size, divide by 4
If you want to eliminate the map type divide by either 6 or 7, depending on whether you picked the string that included the random as an option (pick the nr 7) or exluded random as an option (pick the nr 6)
Wildland Frequency: divide by 5 (non-random) or 6 (random)
Champion Frequency: divide by 4 (non-random) or 5 (random)
Quest Frequency: divide by 4 (non-random) or 5 (random)
Difficulty: divide by 9 (non-random) or 10 (random)
Monster Frequency: divide by 3 (non-random) or 4 (random)
Pacing: divide by 3 (non-random) or 4 (random)
Magic Strength: divide by 3 (non-random) or 4 (random)
Resource Frequency: divide by 3 (non-random) or 4 (random)
Random Event Frequency: divide by 4 (non-random) or 5 (random)
Number of Opponents: divide by 8.
Typical Intelligence of Opponents: divide by 9 (non-random) or 10 (random)
Kingdom VS Empire Balance: Divide by 5 (non-random) or 6 (random)
Opponent Surrender Threshold: divide by 4 (non-random) or 5 (random)
Victory Conditions: Errh difficult...
If you want to exclude the option to start a game with NO win conditions, divide the number by 16, and multiply with 15.
This is my very unprofessional version of your variations.
Hope it helps at least, if nothing else I have provided all the silly numbers 
Sincerely
~ Kongdej