You may want to first explore the possibilities of fiddling with the manual Colour Calaibration panel sliders; and/or, changing the per-RGB-channel settings in (a special copy of) the underlying camera profile, which can be achieved with the free dowloadable DNG Profile Editor.
The "twisted" output from the above, can then be tweaked and re-coloured or desaturated in HSL. I can tell you that it get confusing! - for example, some LR controls might seem to behave opposite to normal.
IOW, maybe you can get what you want by "twisting" the normal function of the software you already have. Or maybe not; it costs nothing but time, to find out.
If it does come to an external program: while Adobe have deliberately crippled Elements so far as access to colour channels and different image modes in concerned, 3rd party lower-cost competitors to Photoshop do not suffer the same constraint.
If calling in such a program to do just a few very specific jobs, and not as your sole editor, the usability and overall range of features of that program are not critical. For example, it does not need to read Raw, be compatible with your LR editing metadata, or output anything - merely receive a TIFF, alter its content and save that again. And you only have to know how to do that particular task, within the program, too; with everything else still happening in LR perhaps, just as now.
Full Photoshop is definitely not the only way; Lightroom can be set up for any editor program quite easily.
RP