Well the way I see it, transsexual people will, before or after gender reassignment, be gay or lesbian.
If I'm a man who likes women, and I am transsexual, and I transition into a female, I then go from being a straight male to a lesbian female.
So before or after gender reassignment, they belong to the rest of the spectrum. They have a shifting sexual orientation because their bodies shift.
I totally agree with your view of LGBTH. I won't discount bisexuals because of their ability to be with either gender, they are as capable of forming relationships and living life like everyone else.
As for LGBTH I call it LGBTS, where S stands for straight. I do believe in an all inclusive sexual orientation spectrum, and I do hope that we're moving towards that. I don't see the need for division any more.
We should be free to be ourselves, no matter where we fit on the spectrum, and to be proud to have the freedom to accept ourselves and others, and most importantly, be proud that we can be honest.
For your part about transgendered people, that one can be confusing. Usually they have surgeries at a young age, very very young to set their gender. It's not gender reassignment, it's gender selection. So usually they just fall into the spectrum based on their gender and the gender of the partners they prefer.
Basically theirs is a gender issue, not a sexual orientation issue. Usually though you see them lumped in with transsexuals, sometimes both are referred to as intersexed.
As for homophobia, it is an old term, and not accurate, but it stuck. Much like how gay equals homosexual, but before gay meant happy. So though the term is inaccurate, and is usually used to define anti-gay sentimentality, it still stuck.
However I personally view homosexuality as a personal view, which I can respect, and which they can speak of respectfully. There is the more extreme version that I call anti-gay, which is when people don't respect us and discriminate against us based on our sexual orientation. So that's where I draw that line.