3-way switch replacement mystery: can I solve it without a meter?
Yeah, you had the right idea about screw color, but worrying about physical position was a dead-end. There's no standard. Every manufacturer changes the screw positions on every model every week.
Don't sweat the differing wire colors.  Wire colors are also completely meaningless in 3-ways since all 3 wires are often hot.   The three colors are due to the limitations of using multi-wire cable.  In conduit, when I pick the colors, travelers are the 2 yellow wires.  There's no Code requirement that &quot;travelers must be color X and color Y&quot; because there are other Code requirements that certain other wires must be certain colors.
The 2 travelers can be determined by the fact that they are always in the same cable.
If all 3 wires are in the same cable, then look for one wire that is hot at all times regardless of the position of the other 3-way - that is common.
If that is not present, then look for the two wires that change hotness when the other 3-way is thrown - those are travelers.
I'm a big believer in marking travelers both with yellow tape. There is no need to distinguish 2 travelers from each other.  But 2 yellows in a box is distinctive.