I bit the bullet and did the .conf file fiddling I was trying to avoid doing, and figured out what I needed to do.
In /usr/share/X11/xorg.conf.d/ is 50-synaptics.conf, which is the conf file that controls the touchpad on the T440p (and others). And in there is this section:
Section "InputClass" Identifier "Default clickpad buttons" MatchDriver "synaptics" Option "SoftButtonAreas" "50% 0 82% 0 0 0 0 0"
That is the default settings for the areas on the touchpad that correspond to the right-click button on the touchpad. After much, much fiddling to get the redefined areas correct, this is what should be copy-pasted in to change the right-click area to be a thin strip on the upper-right area of the touchpad:
Section "InputClass" Identifier "Default clickpad buttons" MatchDriver "synaptics" Option "SoftButtonAreas" "50% 0 0 45% 0 0 0 0"
That is as far as I am capable of taking it at this time, but that gets done most of what I wanted. I'm just reposting it here in case anyone else ever needs to see how to remap the zones on the Synaptics touchpad.