Did you try Qcopy ? It was a shareware tool for DOS.
http://reimagery.com/fsfd/bin/Simtel_DOS_1993 … UTL/QCOPY40.ZIP

As far as I remember, it was able to convert copies to 1.44MB.

You could always simply make a boot disk to do this
I'm assuming your real fdd isa: and the gotek is B:
boot the PC (from HDD, FDD, os version, doesn't matter)

with disk1 in a: type
sys A: b:
this will copy the boot files off your dos 5 disk onto the gotek image.
You can then manually copy the rest of the files from the disk to the image.

Edit - so it turns out it's not that easy. The DOS 5 disks I had needed to be installed (sure there's EXTRACT, but not on diskette 1) and THEN I could SYS the b:\ GOTEK image.

I killed two birds with one stone by installing DOS5 on the second 256Mb SSD and then SYS to the GOTEK cell slot in b:\

DOSSHELL FTW!