I'm about to tell my advisor I want to leave my PhD. Do I mention this when scheduling a meeting or do I drop a bombshell while there in person?

It is often better to wrap the functions in Evaluate[] rather than set Evaluated->True:

Plot[Evaluate[
  logRateApproxListLargeNe[[subList]]], {Δy, -4, 4}, 
 AxesLabel -> {"Δx Ne", "Θ"}, 
 PlotStyle -> Automatic, 
 PlotLegends -> 
  LineLegend[subList, LegendMarkers -> Automatic, 
   LegendFunction -> (Framed[#, RoundingRadius -> 5] &), 
   LegendLabel -> 
    Column[{"Δx", "Approximation Order"}]]]

• You may wish to wrap the Plot expression in Block[{Δy}, (* Plot *)] if there is any chance that Δy may have a global value.