Can vlookup use the far-right column as the lookup value instead of the far-left value?

No, but you can use INDEX and MATCH functions to do that or......

1) You can insert a column to the right of your lookup data.
2) Copy or reference data that was to the right of your lookup data,
3) Hide the new column and do a vlookup as you wanted to do before
This approach is not as "clean" but is a work around for this particular problem

Suggest you use INDEX and MATCH

You can either use some hidden columns that hold the same values as the columns to the left of your search column (simple but a bit clumsy) or you could probably use INDEX & MATCH of perhaps even LOOKUP.