The "obvious" way is to repeatedly run a sharp knife (such as a carpet knife)
along the panel's edges, until enough of the adhesive has been broken that the
panel comes loose.

Some adhesives can be made brittle by cold. Can you leave the Advents
in a walk-in freezer overnight? You might find it easier to break out
the crossover board after chilling the adhesive down to sub-freezing
temperatures. A gentle sideways "rap" with a soft mallet and a dowel
might break it free.

If you do this, seal the speaker in a plastic bag before bringing it
outside to warm up to room temperature, so that you don't get lots of
condensation forming on all of the metal and plastic parts.