I'd better answer my own question. After studying the HGT code I found the relevant HiSoft Basic variables named windx, windy, windw and windh. Not mentioned in the manual, these determine your window size. They are set to your maximum window size by default. Define them as SHARED and use GemAES call wget to find your max window size. (For some reason HBasic's WINDOW GET does not work here.) Use this to adjust the new window to your desired size. Then call HGT's open window call. Like this:
SUB processusermenus (VAL wind,VAL item,VAL title)
SHARED Finished_Flag,MyWindow,whandle,windx,windy,windw,windh
(...)
CASE mnopen
dum = wind_get(whandle,7,windx,windy,windw,windh) 'get screen size
windw=windh 'make the new window square
whandle=OpenTextWindow("Your window title",win_all-win_info)
init
END SELECT
END SUB
Works for me.