Printing strong reds from a painting, to a matte paper, will indeed give everyone headache.
I would start to look for the matte paper with the biggest gamut volume, e.g. Ep Hot Press or BreathingColor Elegance
And your printer is probably the one that gives the "best" reds on the market, with its Vm+LVm+O.
When I know that some of the saturated colors in a painting, never will print "full", I'll skip the saturation part
and look more for the right nuances and luminance.
One thing to cheer up with, is that the original and reproduction never will hang together
/Sven