From what I'd read here, I thought veneer was the way to go, but would want something to prevent splitting.
Layers of veneer top & bottom, and one cross-grain in between.
Or layers of veneer laid ten or fifteen degrees off the bias, so the grain is mostly longitudinal but still keeps things from splitting away.
No one ever said that plywood
has to have sheets laid with the grain at 90 degrees, all evened out and everything. In fact, back when plywood was
the high-tech stuff to build planes out of there were all sorts of grain arrangements.
I'm also concerned with bolting the LG to the model, and axles.
Thinking off the top of my head, I'd say that for attachment you want to bulk up the thickness enough to compensate for the holes you drill, or make brackets that span the gear. You probably want to thicken things up at the axles, too, and you probably want to do it somewhat gradually, lest you just snap thing apart where the doubler starts.