Don't take the proposed modification keys too serious, you can easily exchange Ctrl with Alt to avoid collisions with file sorting for example. It's just a general idea.
In this example Shift always means "without extension", Ctrl always means "same pane". Here we go:
F2: rename filename incl. extension
F2+Shift: rename filename only
F5: copy file, rename filename incl. extension
F5+Shift: copy file, rename filename only
+Ctrl: Toggle for same panel
F6: move file, rename filename incl. extension
F6+Shift: move file, rename filename only
+Ctrl: Toggle for same panel, so that would be the current Shift-F6 for renaming
F7: create new folder
F7+Shift: create new file, don't open editor...
F8: create link incl. extension
Shift-F8: create link without extension
+Ctrl: Toggle for same panel
F8/Shift-F8 for deleting is superfluous (because of del/shift-del), that strange Alt-F4 Exit-key even more, it could be used for some other meaningful operation.
So, what about that? Yep, it's against all odds, I know, but it makes sense at least.

Icfu
Edit: First version had bugs.

Add an ini-setting for easily inverting the BASIC meaning of function keys (with or without extension):
ExtensionToggle=1/0
One setting to specify the preferred modification key:
ShiftCtrlToggle=1/0
That should satisfy most if not all users.