May want to check that a 375ml isn't a disqualifier but I wouldn't feel comfortable sending an unsafe bottle nor does it make sense to undercarbonate and get dinged for style.
If you can send 375ml bottles, the easiest ones to get that will hold that kind of pressure are the stubby Belgian beer bottles like what 375ml Chimay and Duvel come in. You could also find are 375ml champagne bottles but the only way I find those is Lindeman's backsweetened beers. Another option are the 375ml German weizen bottles. They look a lot like standard 12oz bottles but the glass is a little thicker. I don't know if they are rated for 4 volumes but they can probably handle it.