While women in the Military is usually a bad idea because of having to work around menstrual cycles, dual personnel facilities, incidences of rape, and the fact the majority of women cannot drag a 300lb downed soldier from out of the line of fire to a safe spot while also carrying 50lbs of supplies on their back, I'm still of the belief there are some combat positions that they could excel at.
I've seen some studies in the past that indicate women on average (not all) are about 1/20th of a second slower in reaction time than men. The tests come from video games that were designed to measure hand-eye coordination and visual impulse control. (I've been digging for the article, I'll post as soon as I find it.)
That explains why, typically, women prefer not to play games that require snap reaction time like fighting games and shooters. There are some notable exceptions to this, as there are with all things, but it does hinder their combat effectiveness at an average.
In terms of advantages on the battlefield, a woman's small stature and thinner shoulder width are of benefit for tight-confined combat scenarios. In addition, women generally have better precision (not necessarily accuracy) with firearms, as they are far more patient with their shots as an innate compensatory result of their relatively longer reaction time.
What are a few ideas you might have for a good combat troop position (not a desk job) for women to hold that emphasize the strengths of women on the battlefield while avoiding the weaknesses?
Here are some positions I think they would excel at and why:
Sniper
Snipers usually work in teams of two, where a spotter aides in mapping wind patterns, watching where the bullet lands, and other logistics about taking a shot. This alleviates the burden of the woman in having to carry the same kit as men despite not having an equally rigid frame to do so. Have the spotter be a large man, and carry the pack as they already pretty much do.
Long-range snipers don't particularly need to focus on reaction time, as a moving target is nigh impossible for even the best of snipers, and wildly firing at a moving target is a good way to tell your position to the enemy.
Additionally, women's smaller frame, thinner shoulders, and smaller height allows for a better cover scenario when perched in full ghillie suit.
Shooters like Annie Oakley have shown us that some women can certainly excel at this position, and I doubt she was as much of an anomaly as they make her out to be, simply because few women even attempt such a craft as trickshooting.
Pilot/Tank Crew
A woman's small frame allows for easy mobility in tight quarters. Pilots, Tank Crews, even Navy engineering and mechanic positions benefit from this. Also, the smaller frame of women mean a G-suit doesn't have to work as hard to equalize pressure in high-speed aeronautical maneuvers.
Ordinance Defusal
Okay, sure, it's a job no one wants to do, but a lighter female would be much safer than a large man. At least there would be a nominally greater chance a land mine won't trigger because the person stepping on it is 50-100lbs lighter. Also, smaller hands and bomb defusal go hand-in-hand, if you pardon the pun.
Thoughts?
I haven't been in the army, but I do know a bit about it from my own research. I'm not able to join the army, otherwise I probably would have.
Endurance and strength can be modified, but not frame. I think women, if they underwent the proper regiment could meet the requirements you laid out, but they definitely would not be your "average" female, I'll preemptively agree with you there. The psychology of pissing and shitting your pants as a sniper also aren't above the capacity of a woman. Besides, women require less caloric intake and could probably last longer than a man in an attrition situation (I'm speculating on this last point).
I think infantry all around would be a bad idea for women, which you probably agree with. Primarily because of the additional logistical nightmare and psychological trauma if they were captured by the enemy. They would be seen as targets and hunted simply because of their value as a sex puppet.