Okay, I went quick and dirty and made a shim out of a de-spined old GEM blade. Just turned the edge back, it was fully covered by the spine of the current blade, no hazard at all.
Well, it upped the efficiency for sure. 3-pass almost-BBS shave. I'm going to make a 'proper' plastic shim. I imagine, it should be slightly thicker.
Thanks for the insights gents!