The figures, for anyone assembling their own picture. The three numbers to write on the vial: total mg, total ml, and mg per ml. Everything else is division. And the sanity check is that dose volume times number of doses should be less than the volume you put in, because dead space takes the difference.

One thing that is still open after Dr.LipidDallas’s answer:

How much material I am losing to dead space, and whether that explains why a 10mg vial gives me nine usable draws rather than ten?

josh_phd_bmore said:

The three numbers to write on the vial: total mg, total ml, and mg per ml.

There is a second half to this that has not been said yet. Concentration choice is a precision decision, not a preference. Reconstitute high and every dose is a tiny volume where one unit of syringe error is a large fraction of the dose. Reconstitute low and you get more graduations per dose, so the same hand tremor costs proportionally less. Against that, more diluent means more benzyl alcohol and a shorter comfortable in-use window.

Closing the loop on my own question.

Follow-up: it was dead space. Switching to a low-dead-space fixed-needle syringe gave me the tenth dose back.

Dr.RheumBOS said:

Concentration choice is a precision decision, not a preference.

Agreed, and it is worth saying that rounding to the nearest whole unit is usually acceptable at maintenance doses and is not acceptable at the bottom of a ladder, where one unit can be a fifth of the intended dose.