You can forget about getting LTE or even 3G on your international edition of the Galaxy S3. I went to a T-Mobile store in Seattle this morning and talked to a very knowledgeable assistant who immediately knew of my problem and was able to definitively confirm that 4/3G isn't happening.
Why? Because of the radio frequencies in which T-Mobile USA has so far introduced on its LTE network. They're different frequencies to the ones that the international edition of the Galaxy S3 is tuned for.T-Mo USA "might be" building out its spectrum to cover these but I doubt it.
So you have to stick with EDGE or use wifi. Sorry.
Next I went to AT&T in Seattle and they checked the S/N of my handset to confirm that it's compatible with their LTE network. However, their cheapest PAYG network is $25 a month for data and a further $25 a month for voice, whereas I'm currently using T-Mo for $3 a day, and since I'm usually in the US about 4 times a year for a week at a time, it's much cheaper to pay wifi charges in hotels instead of using my Galaxy as a hotspot.
I also asked the T-Mo guys if I could hack the phone just to get 3G and forget LTE. The answer was no - because it's the radios in the device. I think I'll go back to my BlackBerry for 3G while in the US ...