The landing distance chart in the RPL workbook (figure 4 on page 6 of version 2
from 08 November 2018) naturally contains a correction for slope, but I'm
really confused about how to use this in the face of a downward slope.

What is the procedure for using this correction? If I draw a horizontal line
from the pressure height/shade temperature box to the appropriate downward
slope percent and then follow the correction lines down and to the right to the
reference line, that will cause my landing distance required to decrease. But
surely that isn't right -- it should increase for a downward slope, right?

I took an old BAK exam and missed a question because of this, so I'm nervous
about getting it wrong on the RPL exam. Any help appreciated!

Ah, I think I see: it must be that you continue the horizontal line until you
hit the vertical reference line, and then "zag back" to the downward slope
percentage, going upward parallel with the correction lines, before going
forward again horizontally to the wind section. Similarly for tail winds.

Yep, that's correct.

Regardless of the chart presentation used, the standard exercise for the chart designer is to

(a) run the backroom sums (these will come either from flight test or calculated workup validated/refined by flight test) and then draw up a starting carpet (in this case, the boxy graph on the extreme left).

[This gives a set of answers for the reference line conditions in the correction grids. That is, if you run across left to right from the starting carpet ignoring the correction grids and go straight to the final axis scale on the extreme right (distance), you will obtain the calculated value for the reference grid values of slope and wind, in this case, level runway and nil wind.]

(b) then use the basic output from the starting carpet and correct for whatever other variables are considered in the chart. The chart should have example lines for the guidance of users. The examples usually will show only one iteration (in this case slope is 4% up and headwind is 10kt) but the use is generic and should generally be similar for each correction grid. So, in this case, moving left to right from the starting carpet, one moves to the reference line and then to the appropriate variable value in each correction grid. If the calculation, on the day, needs to use, say, down slope or tailwind (for this chart) then the process is much the same but you will move in a different direction from the example line.

Note, if you were, for example, setting out to determine a limiting OAT, knowing the distance available, then you would be moving from the right hand axis in a right to left direction. In this case, you would still follow the example line but you would need to run to the value and THEN run parallel to the guidelines to the reference line before moving on to the next grid on the left.

Just takes a few practice runs to get the idea firmly in the mind ..

You will see all sorts of airs and variations on a theme with performance charts, some simple, some complex. All, however, derive from a similar draughting philosophy in their graphical design ..