Is it obligatory for a woman to exaggerate her covering during bowing and prostration if she prays in front of men, or is it not permissible for her to prostrate in front of them at all?

It is not forbidden for a woman to prostrate in the presence of non-mahram men. It is recommended for her to keep herself compact during her prostration, by pressing her abdomen against her thighs and her elbows against her sides. She should spread her forearms on the ground and lower herself, not raising herself upright as men do.