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Is there a simple, built-in set of keystrokes that will move me between open documents in TextPad?

Ctrl-Tab and Ctrl-Shift-Tab

Experiment a bit with it and notice the difference between

Pressing and Holding Ctrl
Pressing and releasing Tab
Pressing and releasing Tab
Releasing Ctrl

and

Pressing and Holding Ctrl
Pressing and releasing Tab
Releasing Ctrl
Pressing and Holding Ctrl
Pressing and releasing Tab
Releasing Ctrl

Ctrl-Shift-Tab gives you the inverse order of the order used by Ctrl-Tab (which is - as far as I can tell - the order in which you last activated the docs in Textpad, last activated first)

An alternative is to use F11 - the document selector. Clicking on one of the open documents switches to it instantly. I leave it on all the time an flip between the open sessions.