I was also gonna not recommend MDF, but couldn't recall the exact reasons, cuz I don't work with it enough. But putting dollar signs next to it and Birch, implies trying save, what, $40 on a sheet? It's just not worth trying to be that money-conscious when we're talking about, what, half your sound? Of arguably the best-sounding modelers on the market... Kinda stepping over a dollar to pick up a nickel. Plus, you'd already be realizing some savings by building them yourself, depending of course on the value of your own time. And then, some of us don't care about that at all, due to the enjoyment of building them yourself.
There's different factors to consider, but the price of a half sheet of Birch vs. MDF definitely shouldn't be one of them. There's a reason cabinetmakers use plywood for the boxes, MDF for the door/drawer raised panels, and wood for the face frames.