Welcome to HealingWell. I hope we can give you some good advice here.
Since you're in the clear for heart problems, I would suggest asking for Esophageal pH monitoring. This will place a device (either a capsule or a tube that goes down your nose) on a point in your esophagus above the LES. It will record when and if acid is splashing back up into your esophagus and possibly causing your chest pain. Here is the Wikipedia page, which I found to be very informative: http://en.wikipedia.org/wiki/Esophageal_ph_monitoring
It is possible that Nexium isn't the right drug for you, or that your dose is too low, etc. That's another good one to ask - tell him your symptoms, how long you were on the Nexium before, and your symptoms before, during, and after. I personally would need to write it all down, so maybe you would like to also.
I think what's really important right now (in addition to further testing) presenting to your doctor that you're living in pain. You said that he didn't seem to worried - to me, that is unacceptable. I understand if he's not too worried because it's not a lethal condition, but leaving you to live your life in pain isn't a solution. That right there would prompt me to ask the new GI doc what options you have, be it a medication change or whether or not you're a good candidate for surgery (in which case, the pH monitoring is necessary).
It seems very strange for your old GI to tell you that diet has nothing to do with it because for a lot of us, it does. However, if you've tried excluding trigger foods and found no difference, there could be something to that. I would suggest making a food diary to present to your new GI. Not only does it show him what your diet is like and let him make suggestions for changes, but it also shows him that you're actively interested and trying to change your condition. Plus, the whole time you could have been eating something that was bugging you. This is what happened to me - I was perplexed and frustrated because I stopped eating all triggers but still had a myriad of symptoms. Finally I started a food diary and realized that I had problems with dairy. I would NEVER have thought about it without the diary.
Also, have you made any other lifestyle changes? Such as not laying down for 3-5 hours before bed, and sleeping with the bed raised? These "small" things can make a world of difference sometimes, and again shows your doctor that you're working with him to find a solution.
Keep us posted! I'm eager to hear if this new GI takes your plight more seriously.