I don't envy you any of that.
For starters, let me just say that it sounds like you're going above and beyond for this process, which is awesome. It says something about your commitment and academic concerns, but also your confidence as a scholar. All I'll add here is that, at a certain point, there's nothing more you can do. It's frustrating, but eventually the ball's in their court. It sounds like you've done nearly all (if not all) you can.
As for the professor who's not returning your emails, this is a tough one. I typically say that if you've emailed a faculty member and they don't respond in 48 hours, sending them another email is fine. If that one goes unanswered, the best thing to do may actually be to reach out to a department administrator. It can occasionally be the case that a professor's spam filter sends messages into the spam folder for who-knows-what reason. You say you've established contact with the grad director; it probably couldn't hurt to mention you've tried touching base with the other faculty member, and would love to speak with him if possible.
Although this is difficult to gauge, one thing to consider is also how much establishing contact outweighs the possible (albeit probably unlikely) chance of annoying the professor you're trying to reach. For safety's sake, I definitely wouldn't email him again, just in case he has noticed your emails but simply hasn't had time to reply. I also wouldn't call his office phone. In my experience--at best, faculty simply ignore their office phones; at worst, they grumble and complain about getting calls. It's a good idea to try and make yourself stand out from the piles of names they have to sift through, but you don't want to stand out for the wrong reasons. I think your best bet would be to mention your interest in his work to the grad director or another administrator, and that you've tried to get in touch with him. It could be that your messages aren't getting through, he's swamped, not teaching for the semester (or out of the office for some other reason), or that he's just particularly bad at responding to emails (in which case you don't want to get on his nerves). I think going through some other party is your best bet.
Can I ask why Johns Hopkins is fully out of the running? You're applying to PhDs, correct? The professor you want to work with may be going on sabbatical the year you apply, but what's to preventing him from working with you after he comes back? Most doctoral candidates don't really start their dissertation projects during the first year anyway, since they have to take classes full-time--unless your package will be different, since you already have a master's...? Sorry, a lot of questions.