Better check the writing your helmet's face screen.You are looking at this the wrong way. You do need eye protection but a full face screen provides that and more. Safety glasses can be more of a hindrance. A good full face screen can do eveything that safety glasses will and aslo keep the rest of your face intact.
OSHA has this to say about it -
Note to paragraph (d)(1)(vii): The employee does not have to wear a separate eye protection device where face protection covering both the eyes and face is worn.
I just looked at my Premium Rockman. It specifically states that you need additional ANSI Z87.1 approved eye protection. So while there may be shield than can serve that purpose...a forestry helmet faces shield is not it (unless there is another brand that says it can...maybe, but not on the ones I have seen - also looked at my old Peltor). It MUST state on the face shield that it is Z87.1 approved.
Anti-fog/anti-scratch safety glasses can be had for less than $15.
Wear safety glasses under the face mask.