The page says a true veil should hide when you are born, and that this would privilege long-run expected value over present-generation maximin.
The second half does not follow. Someone who maximin's and also doesn't know their generation still maximin's: they protect the worst-off person in the worst-off generation. Bets that might wreck a future floor get rejected harder, not replaced by an average.
Hiding the birth year extends the rule. It does not switch the rule.
Then the work is being done by a second choice: once time is in the picture, swap maximin for expected value plus variance.
Those are already the knobs in §II. Impartiality about when you live does not force the swap. You can refuse to know your generation and still refuse to gamble the worst generation's floor.
The medical-research example only fires if maximin is stuck on people alive now.
If you might be the patient in 200 years, a floor-protector wants the drug that raises that floor. Skipping speculative medicine is what present voters do because they cannot eat a future treatment. That is democratic impatience, not what the veil says once birth year is hidden.
If birth year is hidden, does the chooser ban the research, or fund it?