I thought the older W111 dash grills were screwed on.
I'd be reluctant to pry on a wood speaker grill without knowing for certain what's holding it down. Even if you know it's fastened with clips, sometimes they will have a death-grip after being fastened for so long. (Or a previous restorer may have broken some clips and glued it down!)
Is it possible to remove the radio and reach in through there?

Your AC looks like the standard 'Kuhlmeister' hang-on unit. Usually there's 2 or 3 screws holding it to the underside of the dash. If it was installed to original standards, there may also be a lower bracket securing it to the heater. Can you unbolt the unit, without disconnecting the AC freon hoses, then swing it out of the way?

Happy Motoring, Mark

__________________
DrDKW