I've already checked the keyboard shortcut guide, so this is my last place to look. Are there any keyboard shortcuts to change the color of the fill of a selected path?

no

I suppose you could say there is, if by keyboard shortcut you mean you want to do this without using the mouse or a pointing device.
Ctrl-shift-F opens the fill and stroke dialog and makes it the active window; tab and shift-tab steps forward and back through each option from the top, enter selects an option, and when you get to the numerical entry fields you can enter a number. When you get to the RGBA field you can type in the 8 character hex code for the color you want.
It's keyboard, it's fast, but not 'shortcut' in anyway.

If you just want to avoid opening the dialog, try the gestures from the bottom left hand swatch - click on it and drag up and down to change hue and use control and alt and shift to change other parameters.

It would be neat if ctrl - alt - f clicking on an object opened a little hex code field that you could type in. No idea if that's possible to code into the program very easily.

BTW, two hours is not a lot of time to give people to respond before marking the topic 'solved'!