One approach would be to upload everything, wipe the phone, then log back in but not connect to iCloud (or Google). Once you've cleared the border, go to a cof

One approach would be to upload everything, wipe the phone, then log back in but not connect to iCloud (or Google). Once you've cleared the border, go to a coffee shop and download over their WiFi. Or not, if you're on a unlimited data plan. That has the advantage of requiring only one phone but would definitely look like you were hiding something. So your approach of a travel phone is better.