But I really ought to go to sleep, and would probably think better tomorrow, so for now one answer and one question.
For individual age, it seems that it could become confounded with the time varying covariates. Could you just use "Age at first observation" for each individual? Then use time or its covariates to basically cover the effect of ongoing time. Or is there something about specific ages (eg. reaching ***ual maturity) that is needed.
You say you have observations over 10 years. How many for each female (what's the range?). Are measurements taken in discrete time or continuous, and how often for a single female? i.e. do you measure all females (that you can find) once each month? Or could one be 4 days apart and another 20 days apart?
Do you have more than a full years data on a single female? Are there seasonal variations in the months. What I'm getting at is if you follow the same female for say 4 years, and some covariates or the DV vary a lot seasonally, you might have trouble with treating time as both a linear (as in age) and a circular (as in month 12< month 1) variable. Actually, that might work....
The variable that is nearly constant--is it continuous or categorical?
Anyway, I'll check in tomorrow. Couldn't help myself there.