Sorry, but there is still a solution..
I've heard about the Simplify3D program. I decided to take a look. I installed it, did not configure anything, pressed Ctrl+P and saw a miracle: I select the COM port with the desired printer, print directly, print from a USB flash drive, even write to a USB flash drive! The recording is slow, but it is there and it works!
I didn't like Simplify3D as a slicer. I just generate the G-code in Cura and use Simplify3D print manager to do whatever I want with it. So, all this is possible. No special printer firmware is needed. It's just not in Cura!