It seems like you've already been trying my main suggestions. I'd otherwise start suggesting looking at commercial models.

For anyone else who might come into this thread, or to give my input anyways.

For something new: EZ-DUZ-IT brand. They took over the US manufacturing facility after Swing-A-Way moved to china.

For something used: find used Swing-A-Way openers at thrift shops. I recently picked up a couple at Goodwill for a couple bucks or less each.

Their assembly is the same for new or used. Their gears and blades unscrew from the body and can be touched up or replaced. If rusted they can be touched up with a scotchbrite pad, vinegar, etc. Putting them on a machine screw and nut will let you mount the blade in a drill and touch them up quickly with scotchbrite. You could sharpen them with a file or sandpaper, but that's prob getting into more effort than its worth because...

You can also buy entire rebuild kits online from Sierra Trading for about $9. New gears and blades; direct replacement.

Search here on BIFL for other threads about the Swing-A-Way including photos and details for the repair kits.

Additionally I've had good results with the Oxo Smooth Edge Can Opener sold at Target. It has a single handle, not the split-handle model shown on Amazon or Oxo's website.

But it sounds like maybe you're opening a lot more cans than I am. Maybe it's worth it for you figuring out how to sharpen the swing-a-way blades.