Also, I have to imagine that magic would be treated a bit different than technology (since learning magic is an academic process, then that lends itself to a bit more focused style of advancement than the more mundane technologies that are reliant upon society as a whole to implement).
says who? Its magic! It can be just and random and chaotic then anything else. More so even.
Anyway, the point is that having a strategy that focus on a specific thing is what min maxing is. You maximize one thing and minimize all others that would sacrifice from getting the apsolute maximum on the one thing. If you looked up "min-maxing" in a dictionary somehow, that is what it would say (or something similar with better thesaurus work). It is not a problem by being what it is. The ONLY reason people do not like min-maxing is because in many systems, it creates a flaw in a system. Its like if a wall has a weak spot and you focus all your force into that one weakness, it will break everytime. However, with proper balancing it shouldn't break. A min-maxed strategy shouldn't be more powerful than a well-rounded strategy. Achieving this balance is VERY hard, but it is possible. At this point in the development process I don't think we should be talking about how to avoid min-maxing, but rather how to just achieving balance.
That also being said: that is a different arguement from the inclusion of luck as a major game mechanic. Its not a minor flux in damage rolls, its a major change in tech-tree that would prevent a player from being as specilized as he wants > that is what doesn't seem good
I think a better alternative would be make its so that there would be several top-end techs that are about the same and perhaps have a chance to get one or the other. The strategy for the techs should be un-changed (like both should enhance the same feature) but there is a chance. The only way to get these techs is by min-maxing, and they should be equal power. That way players would still want to focus specifically on only if thing if they choose, but can still get a semi-random responce. Then if you don't min-max your end-tier tech picked from a selection. Still having it random seems like bad form, but it is a comprimise that adds the kind of random end result.
Here is a cheap diagram to express the idea.
Military > Military 1 > military 2 > military 3 ---- Tech 1
\ \ \\
Mil 1 + ind 1 > Mil 2 + ind 1 ------ Tech 2
Tech 3 (only chance of getting if you have near half and half)
same as above > Ind 2 + mil 1 ------ Tech 4
/ / //
Industry > Industry 1 > industry 2 > Industry 3 - --- Tech 5
The strategies for end techs 1 and 2 would be military heavy
strategies for end tech 4 and 5 would be industry heavy
and strategy for tech 3 would be some middle ground for when you are exactly in the middle.
This would increase the number of times you would replay, but not make so much based on luck. There still would be a little, but it would be less than what it sounds like in your original post. Like there could be luck based on which end tech you recieve based on how your tech tree is built.
/* added note: sorry for the slow responce. I did not include comments after that because I was at work while doing this and it took me like 3 hours to get this post finish. I didn't mean to ignore you if you posted something that addresses what I mean */