The arithmetic coder in JPEG2000 is often the culprit for slow encoding / decoding.

GIMP doesn't work well high-precision files, although it's gotten better. Photoshop can deal with these, even very old versions of Photoshop.

Use OpenEXR or HDR output formats and do the tone mapping as a separate step.

Also note that plain JPEG supports 12-bit in the first place.