My opinion is that you should relax and let your mind be at ease. I believe that on September 1st this year you will be on campus at one of these programs starting the next phase of your education, and all this anxiety will be finding entirely new worries to circle around. I graduated from HDS last year and MarX is right that admission is around 40-50%. I don't know anything about the others but I think you're going to be A-OK.
Once you get to wherever you end up, I agree with you that it's important to take language classes, but focus on what you ultimately want to study and think of your master's education from day 1 as a sort of probationary PhD. IMO the easiest way to get into an elite PhD is to take a master's at the same school, work with (take a class every semester with) the person you want as your advisor, and be yourself (and professional) from the moment you meet them to the moment you ask them to write your reccomendation letters. The people I saw succeed in making the transition from master's to PhD were all people who didnt spent excessive time thinking about their PhD prospects but threw themselves passionately into the research and thrived at it because they loved it (and were also all very talented to begin with of course).
I can't guarantee what the schools will decide, but I think you're going to be fine. If your worse nightmare were to come true and you were rejected everywhere, you could come back here and we'd help you figure out what went wrong and you could reapply next year and I'm certain you'd get in somewhere (I'm also reassuring myself here, because I'm very anxious about my two PhD applications that are out right now and I'm checking my email every 5 minutes for the rejection letters). I think results are released around March 15th so you have a month to go. Best of luck! And let us know what happens.
