other than my feeble attempts at 'soft proofing'... how would a person check to see, indeed, whether the colours are within the device's gamut?
Armed with my new toy (ColorThink) I went a-Googling and found a profile for your Epson 4900 printer "Standard Proofing Paper Production V1" (SPPP). As you know by now, any profiles gamut can be displayed in glorious 3D on your screen along with the gamut of your images. I brought up your three images in turn with the SPPP gamut and comment as follows:
In the cactus image there are some deep reds outside of the SPPP gamut, so you would expect some color clipping if you choose relative colorimetric as your intent.
In the ProPhoto image lots
of out-gamut reds plus some yellows and also a few very light reds. You would need to convert this image to sRGB and perhaps perceptual
intent would get you there. Alternatively to that, I have de-profiled a flower shot in ProPhoto, then converted (assigned?) it to sRGB without changing the working file RGB numbers and then saturated it in sRGB as far it will go. There was a hue shift which need about -7 degs to get the color back to near correct. See my post here:http://www.cambridgeincolour.com/forums/thread28893.htm
In the DSC_5616 image some dark reds are out-of-gamut and string of light reds to white are sticking out at the top. A little more processing might fix that.
I viewed all the above in the L*a*b* color model, but the other two models xyY and CIELUV tell the same tale (as they should).
I expect there are at least two experts here who could help you more than I with further remedial suggestions.