Let us know how it works out. My international S3 has been pretty bad with data. I'm constantly getting proxy errors.
Proxy errors have nothing to do with straight talk.
I get them too occasionally, and I'm a regular AT&T customer. Don't get them all the time, just enough to be maddening.
They have to do with the hand-off of tcp connections from wifi to cellular. Some times the phone tries to maintain its connection to the same web sites or services when it jumps to cellular. But with an ssl connection you can't just swap endpoints like that. Gmail, and web use SSL, as do several other things. Moving to an new IP (dropping wifi and opening 3G or LTE) amounts to total route change, which is SUPPOSED to fail to prevent man in the middle attacks.
You can often pop to airplane mode for a second or five, then pop back on line to correct this. I've seen that fail as well, and had to use the RESTART option (hold down power till menu appears).
Also try Settings / Wifi/ Menu dots / Advanced / Auto-Disconnect ON. It seems to help. I suspect the phone properly closes connections and moves more gracefully to another interface (different wifi or cellular) when this option is checked.