How can I reword "cross-gender" so it doesn't sound like I'm talking about transgenders?

Solution 1:

This research has been focused on applications of such theories across geographies and genders.

is what I would suggest from the top of my head.

Solution 2:

The pan- prefix does not have the same connotation, so try pan-gender applications.

Online Etymology Dictionary:

pan-
prefix meaning "all, every, whole, all-inclusive," from Gk. pan-, combining form of pas (neut. pan, masculine and neuter genitive pantos) "all," from PIE *pant- "all" (with derivatives found only in Greek and Tocharian). Commonly used as a prefix in Greek, in modern times often with nationality names, the first example of which seems to have been Panslavism (1846). Also panislamic (1881), pan-American (1889), pan-German (1892), pan-African (1900), pan-European (1901), pan-Arabism (1930).