Perhaps you can use the single gender as a time stamp? Where past-present-future are gendered? Something along the likes of how sign language places time in the front of the sentence (future, me run. Past, me run.).

In this case, I'll use Spanish and let "La" be future and "El" be past. Some examples with Jenny running in a park, "La, Jenny corre en parque." and "El, Jenny corre en parque." and present would simply be "Jenny corre en parque." I'm not counting "corre" as a gendered word because it is a conjugate for correr which is not gendered.

Since in Spanish "juega" is fem present for play, "jugó" is masc past, this system takes the gendered tense off of the individual word and applies it to the sentence as a whole.