This process sounds very interesting and seems that it might lead me to an answer as to what is the cause of the anemic prints. I would certainly try it if I understood it fully.
A profile is meant to be a model of the device (i.e. printer) behavior. You describe a problem that appears to be related to the model or the workflow that is using the model not describing the device behavior. So drilling down means figuring out if or where or how the device behavior and model or workflow deviate.
So a printer ICC profile typically contains two models/tables, one describing the native (i.e. forward, i.e device values to color, AKA A2B table) behavior of the printer, and for performance reasons an inverse table (i.e. backwards table, reverse table i.e. color to device value, AKA B2A table). In a typical printing workflow it is the inverse table (B2A) that is used to translate the color of the source (i.e. the source image device values converted to color values by using the source images color profile forward table).
So if it were me (of course), I'd use
xicclu to interrogate the ICC profile. You need to be cognizant of the encoding/ranges used, and the direction and the intent you are using. If you are checking against measurement values, you probably want to use absolute colorimetric intent.
To check the forward table, you might want to use:
xicclu -ff -ia -pl profile.icc
To check the backward table, you might want to use:
xicclu -fb -ia -pl profile.icc
If you suspect that the problem may be a disagreement between the forward and
backward tables, you may want to check the reverse lookup using the inverse
of the forward table:
xicclu -fif -ia -pl profile.icc
Note that by default, the device ranges are 0.0 .. 1.0, and that using -pl that the color/CIE/Profile Connection Space values will be in L*a*b*.
Of course if you are not familiar with running command line software, you may have to look for other tools to interrogate the ICC profiles.