A very unfortunate price increase, indeed.
When I bought items in the US and had them shipped to where I was living in Sweden, USPS was (to my knowledge) always the cheapest option.
However, shipping items within Sweden was sometimes cheaper with DHL or Schenker, so when I learned about the price hike, I looked into these companies. Unfortunately it seems to be a lot more expensive to ship items internationally with these two (and their locations seem to be quite scarce here in the US), so my guess is that despite the price increase, USPS is still the cheapest. :/
There might be other options that I have overlooked, though.
Gone but not forgotten - Menasor