Also, I don’t feel like I have a gender because I simply don’t engage with society in a way that would allow for gender,

No, it's because you're comfortable with your gender. Thinking you're too enlightened to be concerned with gender is again, patronizing as fuck, implying that trans people just care too much about things that don't matter.

If someone could accurately explain what it feels like “to be a man/woman” without bringing gender roles into it, I feel like I would be able to understand that.

You're actively trying to not understand it. Being a man/woman is simply a matter of being treated like you would any other man or woman. And I know you're going to respond with "I don't treat people differently". Even if that were the case, which there's no way that's true. Even if you were 100% bisexual, attracted to both genders identically, and really could ignore 10s of thousands of years of cultural history, that's not what most people want. Even if YOU could, most people prefer there to be gendered differences. There are just some inherent biological differences. No one is saying people's roles should be defined by their gender, or for limiting people of any gender to express themselves any way they see fit. But if you're saying that football or hockey or boxing aren't inherently masculine, then I don't know what to tell you.

we as a society and as a movement should choose not to engage with bigots who perpetuate gender roles, such as not working for companies that have a wage gap, and not dating people who won’t let you wear the clothes you want. In this way, we will eventually force people to accept that the genders are equal in all ways, thereby eliminating them as a necessary construct.

Those are forced gender biases, not necessarily roles. Unless you're saying that it's possible for everyone to be 100% bisexual and have no preference whatsoever for gender in any way, then your whole argument is missing the entire point, just so you can proclaim you "don't see gender". It's similar to how racists always say they "don't see race".