But, then, when I go to the other switch at the other end of each circuit,
how can I tell which wire in each of those boxes goes to the hot "common"
screw? Once I know that, I can connect that hot common wire to the black
"common" screw and just connect the other two wires to the traveler screws.
But, how do I know which of the 3 wires goes to the hot "common" screw?




I would suggest by process of elimination. Using the pic at Option 8.

After you identify the incoming Hot, get first switch installed, then
the "red" or "white" at the 2nd switch will become hot, depending on
position of first switch. The black at the 2nd switch will stay cold
regardless of pos. of 1st switch.

Of course you want all the "loose" wires clear and not touching anything.

Do not assume that the first incoming Hot is in the downstairs boxes !!