Pray tell me if adiyen can recite Prabandam and Purvacharya slokas during the menstrual period as adiyen feels tormented for not being able to recite during that time.

No one must not recite Prabandam and Purvacharya slokas during that period.
Notes:
As we are traditionally trained to chant slokas from our younger age, they are in our mind always and we cannot control them as well.
But during periods one should not chant them aloud.