I agree with GD70 Zpoxy is great stuff drys fast and the particle board soaks it in to make a great bond. You could pick up a couple of hand clamps (Milwaukee brand) about 4 bedrock bucks each at the Depot and once you apply the epoxy you can use the hand clamps to close the gaps. As bad as that damage appears it's really not hard (even with limited tools) to fix. Your goal is to keep moisture out of the cracks so the particle board won't swell. Another good product to use on those damaged corners is Mohawk wood epoxy (putty). Just sand the corners smooth, put some wood putty on them, and sand them smooth again. Looks like finishing nails in the top by the rabbits, if so, can you work them out? If so, would be good to get them out, and replace them once you sand the rough edges and can replace the finishing nails in a different spot. If removing them causes more damage, then just leave them in, the zpoxy will work to hold the top together along with the old nails.
https://www.amazon.com/Mohawk-Finis...=1519127752&sr=8-9&keywords=mohawk+wood+stick
Several YT vids how to use the stuff.
Awesome you posted pics Matt. It's great having documentation of the grills on these model Lxx30 speakers! Thanks for confirming the virtical rods were metal. I suspected that but didn't confirm. I know I can get those at Home Depot in aluminum. I also don't want to miss the opportunity to appreciate how you were able to save the fabric for a template. Those 2030's went to the right man.