I would treat the pine just like any other material for bracing, gluing and assembly.

My Home Depot sells a Chinese made plywood for $30/sheet that is constructed as well, and has more plies than the oak and birch for $45. I've used it myself with good results.

The laminated pine doesn't need edge-banding or miters to hide the edges as plywood does and looks good. The downside is that even with the laminations, it won't be as stable as plywood.

Each time I cut up MDF I swear it will be the last! Too heavy and the dust! Then current local price of $20/sheet means even larger speakers cost only $ 20 more to build with the Chinese plywood.

Call around to some local cabinet shops and ask if they would order an extra roll of birch or maple edge-banding for you. A 250' roll costs them about $35 and will see you through several pairs of speakers. It just irons on the exposed edges of the plywood. Remember to adjust the size of the other pieces accordingly, it's about 3/32 thick.