At the same time, it makes me wonder even more if the Major's original organic body may in fact have been male, with little to no adaptation discomfort after the procedure...
If you read the original manga and got the pages to fill in the abridged portions from the English version, then you wouldn't wonder about it. The Major was originally female.
It's one of many themes about what defines our humanity amidst the cybernetic changes that the manga successfully explores (albeit circuitously in many cases) where all of the animated versions failed miserably (as in the original manga is not "hyper-complicated trash").
The specific sequence for this is one in which the Major is enjoying some virtual vacation time with two female friends. Batou jumps into the Major's head to inform her about developments of an op-in-progress.
The abridged version has the Major and her two friends enjoying time on a boat on the water. When Batou jumps in, the Major berates him for the serious interruption and back in the real world he looks appropriately beaten-down.
In the un-abridged version, the Major and her two friends have moved into full-on girl-on-girl action. Batou jumps into the Major's head in the middle of this and almost loses his real-world lunch since the sensations are ones that a guy shouldn't be feeling and are rejected by his brain.
And, oh yeah, the Major chews out Batou because he was told not to jump into her head during downtime. Back in the real world, Batou looks appropriately beaten down.