Have you seen FilterRules[]? For instance,

Graphics[g, FilterRules[options, Options[Graphics]]]

passes only options for Graphics. Here's an example:

ndsolvePlot // ClearAll;
ndsolvePlot // Options = 
  DeleteDuplicatesBy[Join[Options@NDSolve, Options@ListLinePlot], First];
ndsolvePlot[sys_, y_, dom : {_, _, _}, opts : OptionsPattern[]] := 
 With[
  {sols = NDSolveValue[sys, y, dom, 
     FilterRules[Flatten@{opts}, Options@NDSolve]]},
  ListLinePlot[sols, 
    FilterRules[Flatten@{opts}, Options@ListLinePlot]] /;
   MatchQ[sols, _InterpolatingFunction | {__InterpolatingFunction}]
  ];

ndsolvePlot[{y''[x] - x  y[x]^4 + y[x]^7 == 0, y[0] == 1, 
  y'[0] == -1}, y, {x, 0, 10}, Method -> "ExplicitRungeKutta", 
 Frame -> True]

ndsolvePlot[{y''[x] - x  y[x]^4 + y[x]^7 == 0, y[0] == 1, 
  y'[0] == -1}, y, {x, 0, 10}, Frame -> True, PlotRange -> All]

If you want the default settings for options for the custom function ndsolvePlot[] to be different than the defaults for the components, NDSolve[] or ListLinePlot[], then the FilterRules[] calls should look like this:

FilterRules[Flatten@{opts, Options@ndsolvePlot}, Options@NDSolve]
FilterRules[Flatten@{opts, Options@ndsolvePlot}, Options@ListLinePlot]

Note I did not handle conflicting option values above. For instance the default InterpolationOrder option values are different. The one for ListLinePlot[] is InterpolationOrder -> None and does not work in NDSolve[]. And the default for NDSolve[], InterpolationOrder -> Automatic does something different than None in ListLinePlot[]. In an actual application, one might have to fiddle with the values to get the desired behavior. For instance, one could hard-code the respective defaults like this:

FilterRules[Flatten@{opts,
 InterpolationOrder -> Automatic, Options@ndsolvePlot}, Options@NDSolve]
FilterRules[Flatten@{opts, 
 InterpolationOrder -> None, Options@ndsolvePlot}, Options@ListLinePlot]

Well, I'm think of higher level plotting functions that say things like "ListPlot has the same options as Graphics, with the following additions and changes:" I assume that ListPlot calls Graphics and therefore must doing something similar to what I was looking for: it has its own set of default Options for some Graphics options, which it must pass to the Graphics call, but must let those be overridden by anyone's specified options in the ListPlot call.

Or am I understanding it all wrong?

Well that does work! Many thanks. Out of interest, do you (or does anyone) know if this is how it is done in the built-in functions that have extensive option pass-though (mainly graphics plotting)?