if you just need to receive short codes to your North America number, port your number to NumberBarn. They will forward your SMSs (and voicemails!) to your email.
All I needed to open an account at Krungsri on a tourist visa was my "lease" agreement from the dormitory I was staying at, my passport, Thai mobile number & a big wad of cash to deposit. I brought a Thai friends with me to translate, but other than that it was pretty straight forward.