Mr. Detail - I have had similar slipage problems on a couple of 740s that I have owned.

The arm lifting off the windshield is a fix as described by the other posts.

The slippage is another matter. Indeed, you can probably get a new arm and fix the slippage properly. Just be sure to clean the knurled portion of the spindle with a STIFF brush, like a small steel wire brush. You must remove any of the cheesy metal that has been reamed off of the old arm. This cleaning should be done as part of any fix you choose.

The arms look much too different to swap.

Fix 1 - Add a washer below the nut that holds the arm on. You can do this if the damage to the arm is slight. The washer pushes the arm down on the spindle. This has worked on two of three instances that I have suffered.

Fix 2 - Wrap some fine wire around the knurled portion of the spindle. This increases the diameter of the spindle allowing it to fill the oversize hole in the arm. I had good results with copper wire because it is crushed a bit when you tighten the nut. Some othe material might work as well.

Lastly, prevent slippage by clearing your windshield of ice before using your wipers. And ALWAYS shut your wipers off before you shut off your engine. Frozen wipers put a lot of stress on the connection between the arm and the spindle. Starting your car with the wipers on, or in any location except parked will cause the dust and dirt that has settled on the wiper blade to be scratched across your windshield.
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2 8s & 2 7s 700,000 miles total