To answer the original question, PTGui allows you to copy stitching settings to a new project.
Simply set up the stitching with one set of exposures (e.g. the 15 second exposures), generate the stitched output image, and save the PTGui project file (File>Save); this will yield a file with a PTS extension.
Now copy the PTS file to a new name, and edit the copy in a text editor. Some ways into the file you'll find the image file names on lines that begin with "#-imgfile"; for each image file, replace it with the corresponding file that was created with a 60 second exposure. Also, find the line that begins with "#-outputfile" and change the target file name, so that you don't overwrite the stitched output file that PTGui generates for the 15 second exposures when you generate the 60 second version.
Save the copy, load it into PTGui, and you should be ready to generate your stitched output file for the 60 second exposures.
There may be an easier way to do this (i.e. something within the GUI), in which case I'd be interested in hearing about it. But this has worked very well for me thus far.
Hope this helps!