Oops. I was too quick this morning. More careful observation, and a greater enlargement to make it easier to be precise, shows that I've got the too high contrast visible also to the Spotmeter. Richard Ross from RH Designs suspects it's a combination of flare and the Callier effect, and it seems he's right. It turns out that I can measure relative densities in 4"x5" negatives with the Analyser Pro either by projecting them through the L1200 (a condenser enlarger), measuring at the baseboard, or by carefully holding the negative in position over the Analyser's sensor, using the enlarger without a negative as a convenient light source. Measuring the projection yields a 1.5 log density difference where direct measurement of the negative shows 1.0.
Ah, and according to the internet (e.g. at Dead Link Removed), the average Callier coefficient is 1.4 ± 0.2.
I think I'm going to have a piece of frosted glass made, to fit in the filter drawer, turning the L1200 into a diffuser enlarger for the purpose of such measurements.