Hoorah! Fixed! Please close this bug.
The upgrade of X from 7.0.0 to 7.1.1 (downloaded from Debian testing on 2006-10-27) fixed the problem.
Both video cards work, and the int10 POST of the second card works. Yeah!
I did notice that the second monitor (on the ATI Rage 128 card) now has a vertical sync problem (slowly vertically rolling screen), but it’s an ancient monitor. I might try tweaking the monitor’s internal sync pots or the X mode lines a bit.
Many thanks for the int10 fix.