I think that if you choose any of the four options before you get in to similar sitation that is not strategic thinking.
Since we are talking about million men army and battles I will presume that we are talking about a conflict that happened hundereds of years ago. Since in modern times their spys , air force and cruise missles would probably kill you as soon as the fronline collapses. (If there is even a front line.)
The option about running away can be good if the battle was somewhere in the wildernes and you have a horse. But if it is open field then you can just hope for the best that you will manage to get away. But if there is alot of vegetation and hills you have a realistic chance. After you run away you can freely start ploting something.
I mean if you don't have any means of escape it is not strange that you lost the war in the first place. Actually you have deserved to lose it.
The argument about killing a first soldier is unrealistic. Since back then there wasn't individual soldiers since groups were dominant form. Plus if you manage to actually do this there is a realistic possibility that the uniform will not fit. So if you look guffy in that uniform you will be suspicious. Also if you kill that soldier in a too massy way the uniform will be complety bloody what could look suspicious a well. If there are large physical differences between nations this will probably not work as plan. In the modern times this option is technically pointless since it is well known how enemy leader looks like.
Also there is a big difference in the context on the situation. Since it is not the same if you are the one who started the war or you are the one that is defending his/her country. Also it depends what are the relative stranghts and philosophies or both sides. If you are the one that started the bloody war you are screwed for sure. However if you are the attacker you have certain strategic options that defenders usually don't have.
What means that if you are a good leader you will probably not even end up in this situation.
But if you are not the attacker and you have been attacked by much stronger opponent which has imperialistic tendencies you have one more option. Which is that you demand/go straight to the enemy leader(s) and give them an offer. Which is that they will suffer additional loses if they kill you since they have defeated the oficial army but they will have large problems in controling the the territoty since there is alot of small and tiny
settlement so their large army will have a problem taking control over all of it.
And if they decide to go with totally brutal strategy they are risking a state wide guerilla warfare. Which means they will have to fragment their army to defeat the enemy. Which will make it even more easier to defeat them or create huge loses for minimal achievement. Plus they will have problems with supplys in this case as well and if they kill too much people the terriory will become unproductive for years, plus someone else could sattle in as well without too much problems. The logic is basicly very simple since it comes down to the logic: Every soldier that survives this day can do his duty tomorrow.
Which means that if something happens to you their chances for real victory are slim. Since they can't control the territory if you are dead. To return the favour you promise that you will provide food, shelter and taxes to them/their troops.
This is a risky move from your side but the fact is that this could be the bast chance of keeping your head on your shoulders. Plus you will actually keep some of the power while you wait for better days. Since organizing some real resistance would be suicidal on your part because their people are everywhere.
At least not until things settle down.
This is my answer in short.