Those bridge posts typically have too much of a gap between the support ridges. Unusual to find one that has them too small! Adam should be able to sort you out, though I'd be very tempted to upgrade the bridge.

Most veneer sheets are about 0.6mm thick, so it's worth at least getting hold of some and trying it in the gap. I've got a much bigger gap on my ESB-4 kit, which man even need a veneer sheet on both sides of the pocket. You can always sand the veneer a bit thinner before cutting it out and gluing it on.