So I unscrewed the base.
And unplugged the two leads from the slot selector switch.
If you look closely you will see a raised whitish bump above where the metal arm goes into the plastic. This is why the lever can wiggle, as it has broken through the plastic. Bad engineering!
This is how it should look.
This is how it is when pushed down. This prevents the switch from locking the toaster and starting the cycle, as the lever hits the circuit board below, preventing the toast carriage from travelling down as far as it should.
My first thought was that by shimming out the lever arm with some thin steel strips, it would spread the load on the plastic and prevent it from wiggling.
All that happened was that it still wiggled, and finally broke off the lever retaining piece from the plastic assembly.
So in a last attempt to fix it, I resorted to JB Weld, which is a wonderful metal filled epoxy. Their website shows it as resistant to heat of 500 degrees F, which should be fine for the toaster.
I mixed up a dollop.
And filled the slot.
I reassembled the toaster and inserted the lever, making sure it was oriented correctly. I let the epoxy harden for 24 hours.
The proof is in the pudding, or rather the Nature's Path Organic Toaster Pastries, Strawberry Frosted , which I was able to toast to perfection as a companion to my afternoon coffee.