My solution, which so far seems to work, is basically to rename EVERYTHING. After I created a duplicate install called mod_jw_srfr_1.1_2.zip.
In my text editor I did a batch search&replace to change any instance of mod_jw_srfr to mod_jw_srfr_2, including file names and directory names.
To solve fatal errors, I also had to change simplepie.inc to simplepie2.inc, and I changed any instance of "SimplePie" and "SimplePie_" to "SimplePie2" and "SimplePie2_".
I left the logo file name the same.