Having a good single-pigment green in your palette will save just about any palette, I've found. Phthalo Green (any shade) or Viridian are highly useful. Especially if the green shade is very saturated to unnatural degrees, because they can be muted with just about anything.
I actually did some experimentation on the secondary palette (3 primaries and 3 secondaries), and found that good coverage can be done with just a red-magenta (such as Quinacridone Rose), a cool yellow (Lemon Yellow, but Hansa Yellow Light should also do the trick), a darkish cyan (phthalo blue green shade works, but the red shade also works), and a saturated green. Magenta and yellow can make anything from orange to red to red-orange, magenta and cyan will get you all the purples you need, and the yellow and blue will generate realistic greens (in fact, forest green, hooker's green, and sap green style hues are all obtainable).
Rounding out the palette with an earth tone to more easily mute any color mix is helpful. For me that's permanent brown (which is actually a dark earth red, more intense than burnt umber or burnt sienna). I know you don't like permanent brown but perhaps try it with these fellows, if you still have it. :)
I have both organic vermillion and indanthrone blue, they are very lovely. You can create indigo-like shades with these two. I'm very fond of phthalo green blue shade, and mixing it with a little cool yellow produces an approximation of the yellow shade. (And I create an approximation of gamboge with a lot of cool yellow and a little organic vermillion to warm it up.)
Having a good single-pigment green in your palette will save just about any palette, I've found. Phthalo Green (any shade) or Viridian are highly useful. Especially if the green shade is very saturated to unnatural degrees, because they can be muted with just about anything.
I actually did some experimentation on the secondary palette (3 primaries and 3 secondaries), and found that good coverage can be done with just a red-magenta (such as Quinacridone Rose), a cool yellow (Lemon Yellow, but Hansa Yellow Light should also do the trick), a darkish cyan (phthalo blue green shade works, but the red shade also works), and a saturated green. Magenta and yellow can make anything from orange to red to red-orange, magenta and cyan will get you all the purples you need, and the yellow and blue will generate realistic greens (in fact, forest green, hooker's green, and sap green style hues are all obtainable).
Rounding out the palette with an earth tone to more easily mute any color mix is helpful. For me that's permanent brown (which is actually a dark earth red, more intense than burnt umber or burnt sienna). I know you don't like permanent brown but perhaps try it with these fellows, if you still have it. :)
I have both organic vermillion and indanthrone blue, they are very lovely. You can create indigo-like shades with these two. I'm very fond of phthalo green blue shade, and mixing it with a little cool yellow produces an approximation of the yellow shade. (And I create an approximation of gamboge with a lot of cool yellow and a little organic vermillion to warm it up.)