SOLUTION 100% working so far as I can tell:
Add a 1x1 sprite, name it CursorLoc, Visibility at start: Invisible.
Add two lines of code beneath the globals, before anything else (in this order, too, since it is picky):
Touch is in touch: set position to (Touch.X, Touch.Y)
Touch on any touch start: set position to (Touch.X, Touch.Y)
Replace
"Cursor is over invSlot" with "CursorLoc is overlapping invSlot" (etc, equipSlot as well)
"Mouse Left Button is NOT down" with "Touch is NOT in touch"
"Click on Item" replace with "Touch on touch object Item"
Replace all actions where "Mouse.X" or "Mouse.Y" are with "Touch.X" and "Touch.Y". (These are mixed in with algorithms, just change the Mouse to Touch)
EDIT: In order for the stats to work (see "STATS" group of events), just change it to "Touch Is in touch" instead of "Mouse Left button is NOT down". This works almost as needed: it displays the stats while dragging the item about. If you drag an item and hover over an equipped item it will display the stats of the lesser item if it's equipped (as expected). Moving a lesser item over a more powerful item only displays the lesser item's stats. The desired goal is to have the stats of a more powerful item over it instead. This isn't necessary for me as stats will all be displayed elsewhere, but if you need it, know that this bug is there.
CAPX: https://dl.dropboxusercontent.com/u/11127546/inventoryTOUCH.capx