You wouldn't need to create a new image format. You could use the netpbm portable graymap (PGM) format. All you have to do is add the header "P5\n#Bayer Raw\nwidth height\nmaxcolor\n". The rest of the data remains exactly the same. 16 bit isn't standard for PGMs though. GIMP won't open it, but IrfanView will and so will the Gnome image viewer.
I only had to add around 10 lines of code to do this, and I didn't modify anything. I believe rawconvert can go backwards as well converting back to .crw. I didn't try to modify the code to back convert from .pgm.
Edit:
I just learned that 16 bit PGM should be stored as big-endian. rawconvert outputs the raw data in little-endian so simply adding a header to the data isn't enough to make it a standard PGM. This caused me a lot of confusion when comparing the output of rawconvert with the output of dcraw (which outputs standard big-endian PGM). However, there is a utility that will convert raw data in little endian to a big-endian PGM. It's called rawtopgm. Here's an example:
./rawconvert -10to16 -w=3336 -h=2480 -noshift myraw.crw myraw.raw
rawtopgm -bpp 2 -littleendian 3336 2480 myraw.raw > myraw.pgm