Actually, a slight gap is far better than a slight overlap. I've found that the overlap needs to be more than 1/4", preferably more than 1/2". If it's too small, the overlap kind of "tangles" in the back (i.e., it tries to lie on top in one part of the pleat in one place but under in another part), and the pleats don't hang well. If the overlap is half and inch or so, the pleat knows what to do, and the overlap stays consistent and stable from bottom to top of the pleat.

And, as Steve points out, a military box pleated kilt is simply a box pleated kilt with such a large overlap that it becomes an underfold.

I am confused, though, why basting isn't working to hold the pleats. I put 4 horizontal lines of basting across a box pleated kilt, and I haven't had any trouble keeping the pleats straight for pressing.

Oh - and one more thing. A box pleated kilt should be pressed a bit more lightly than a trad knife pleated kilt or a military box. If you have any gap between the pleats, the gaps will ghost through the right side of the pleats as a "valley". Pressing lightly avoids this.