Any recommendations on an good quality acoustic foam/padding for speakers placed inside of custom cabinets in the front of a theater?

Preferably something that you have used yourself and found to be great for echo resistance, vibration dampening, etc.

Where are you getting echo ... in the theater?  Treating the walls will help you more that treating the cabinet.  Search under acoustic panels.  use the rule of thirds on choosing absorptive or diffusive.

Vibration ... I am guessing that you are getting from the sub.  Do you have a front firing sub ... and a cut out in the cabinet (acoustically transparent fabric? ..... if so a rubber matt works well in absorbing the vibration.

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