Changing passport too
Don\'t worry, I\'m changing passport too because it was going to expire in a couple of months and wanted to have the stamp on the new passport so I will have to carry only one when I travel.
If the H1 is on the old passport, just staple the two passports together and travel with both. I\'ve done that in the past while on a L1 visa , and then on a H1 and there\'s absolutely no problems except the passport is thicker and doesn\'t fit well in your pocket.
Smile, it will soon be over and the stamp will be on the valid passport and youll be able to throw the old one out.
For all those worry for the changed message; just look at the trend, it takes 7-8 weeks after FP done, the message is a good sign that you are just close to be assigned and out of this mess.