Here's how we do it. I prefer a solvent-based birch over MDF. But if its resin-coated, it shouldn't get wet in this application so use your own discretion. Make stackable 1/2" and 3/4" inch thick birch spacer rings. Split them into two equal pieces for easy insertion and mounting behind the foam. Drill and countersink serveral pass-through mounting holes in each half. Resin-coat the rings. Screw the right combination of rings in place behind the foam in order to obtain the correct depth reduction. Pull the vinyl tight into the opening and terminate it's edge by stapling the vinyl into the edge of the birch rings. This will keep the vinyl from pulling or receeding from around the speaker later. Burn through the vinyl and foam with a soldering tip so that the drill bit or screws do not get caught up in it during installation of the speakers. As a precaution, it doesn't hurt to drill in reverse. Predrill pilot holes into the birch rings and screw the speakers into the rings through the foam. The rings will limit how far the foam compresses and thereby eliminates wrinkles in the vinyl that would otherwise appear as you tighten the speaker down.
If you have an aversion to birch then you can use HDPE instead, although the staples won't grab as well.