I share the same feelings. I've spent a lot of time trying to develop workarounds. Unfortunately, I've found, the phone is such a core component of most working life that we're really stuck with it.
Gemtun and the others bring up great points.
I think the issue here is not that you're deaf, but rather, that the TTY and Relay are "strange" -- people don't understand them, people don't know what to do. This situation creates problems. People go, "Oh, yeah. Yeah. Yeah" and then they hang up.
The issue (sometimes) isn't the fact that you're deaf. Many times, I've found, people are friendly and understanding when they realize I'm deaf. The key is that they realize I'm deaf in a way that doesn't catch them off-guard (like a relay call).
Think about it this way: if you see a man in a wheelchair trying to get past a door, your first instinct might be to help him open the door. It's not a pity thing, it's a courtesy thing. This same thing applies to deafness. This same courtesy effect helped us get laws that protect us.
So, I find, the first and most important thing to always do is to make sure the other people realize you're a deaf person. Once they realize this, the courtesy effect makes the situation easier, and people start to become more comfortable with calling through Relay. It's like what Cheri and the others say: meet in person.
Though, if they're just giving you a hard time because you're deaf and not because they're confused, that's not good at all. But don't you ever give up. You have a lot to give to an employer who will recognize you as who you are. 
