I remember that once I had to export this kind of files. You can convert it using arithmetic operator - multiplying all the image by two, substracking or adding 32768 etc. I do not remember exactly the procedure, but with the method trial and errors it is possible to find it.
Other way is the use of a look-up table which will convert the positive values higher than 32768 to the "negative" ones (btw. 0 and 32768).
If you send me a 16-bit tif file you need to convert, I can try it and describe the procedure more precisely.
Regards
Ferda, Ferda_Mr@seznam.cz