Pull your speakers up so they are at least
slightly in front of that cabinet! Please.
AC Infinity Aircom T-10 is a front venting unit with Smart Controls that you can add in with no other concerns. You must keep those doors open when in use, and until it cools off or you WILL cook the electronics.
Getting Crafty:
AC Infinity also makes a lot of other cabinet cooling solutions (and rack cooling too). If you wanted to cut ventilation holes and fit grills and fans, you can.
Intake low. Exhaust high. Vent fans at each location pulling in and pushing out air respectively. You would still want something on top of the AVR to help pull fresher air up and through it, and AC Infinity has those two, along with controllers to help manage the fans. You will also need to consider perforating the shelf the AVR sits on so that fresh air intake can help the AVR.