I had to think about this for a few moments as I agree with a few things the OP says, such as we don't necessarily have much in common with the LGB community, the transgender community spans across the LGB spectrum while still having it's own unique spectrum. But, something about the stance presented strikes me as off, please understand I am not attacking anything posted. Willth that said, I think there is some confusion on terminology in thinking gender and sexuality are related, gender and sexuality have nothing to do with each other. Gender is in reference to being male or female, such as CIS female or CIS male, transgender males and females are across the gender spectrum from CIS males and females, it does not determine sexuality. Sexuality refers to whom you want to sleep with, the only time LGB comes in to play with the transgender community is if a trans person is attracted to the same or opposite gender.
What strikes me off, please understand I believe you are able to identify as you wish, but please understand that arguing that a transgender female, (using self as an example) attracted to females doesn't fall under the lesbian category because I once lived as a male, destroys the stance that trans women are women, trans men are men; even worse, it gives credibility to the opposing argument that we are just men in drag, pretending to be females. I may have lived my life as male but, I have always been female. This may sound like a petty statement, but our opposition will take every miss cue, word, or statement and beat us over the head with it to show we are not what we say we are.