wenwell
Regarding randomness: it's not so significant that it would be impossible to complete the final stage without using the window-opening trick. You mentioned using randomness in the tactical phase. I'll add that this allows you to manipulate randomness in the same way as with windows – one creature animation = a change in the random number. Of course, it won't be possible to control randomness throughout the entire battle as it is done with windows, but it is quite possible to select, say, 2 initial morale values for the desired stacks with a +3 bonus, and then simply disable the fixed randomness or slightly change the order of actions and find not +2 morale, but +4/5, which is quite enough to defeat the boss without windows. Morale here is a conditional concept; rather, it refers to AUM (abilities/luck/morale), using terminology from HP.
Here's an example of the initial phase with opening a window once:
https://www.youtube.com/watch?v=9bo2xeKLYCo
The window could also have been skipped, and simply switch to standard randomness and catch luck in the usual way. Morale for the birds is not mandatory, but it can also be easily obtained.
It's clear that with or without the window, it's all about controlling randomness. The problem is that if we set ourselves within certain rules, with this set of troops, we may need money for another bribe (which, again, does not negate the question of the 5th month). In the case of exploiting randomness, it is possible to complete it with only one bribe, but perhaps an additional stack of "cannon fodder" will be needed in the first stage.
And I'll also note that in both cases, we're talking about playing with snake generation, which gives a much greater advantage on this map than messing around with creature animations.