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Does TheBat have a way to do a redirect via a rule?

Yes.

Account -> Sorting Office -> Incoming mail
Press the 'new filter' button
Give the newly created filter (what OE call rules) a proper name
Click on the 'sender' bit of the condition and change it into 'recipient'
Let it match your old address
Go to the 'Actions' tab
Select 'Redirect the message' from the available actions by double clicking on it. (You'll need to scroll down a bit before you find it)
You'll be prompted for an address to redirect it to. (The box with three dots will let you pick one from the address book)
Press 'OK' and you're done

There's hardly anything that TB can't do with filters, so go ahead and experiment with them.