I took this as a hint. The original garbage disposal was a InSinkErator 1/3 hp Badger 1. Tonight, I purchased a InSinkErator 1 hp Excel model which I'm hoping will eat pretty much anything we want to throw at it. Supposedly, a replacement garbage disposal is easily installed by one person. However, it apparently is very useful to have a second person handy to help hold the thing up while doing the installation. (The recommended alternative appears to be building a stack of books to hold it up. Thank you, but no. I like my books.) I considered having it professionally installed if it didn't cost too much, but I carefully checked with samwinolj to see if he were available to help in case of obscenely high installation costs.
$150 was well into the obscene range, so I've officially asked Sam for the favor.
We'll see if $150 still seems obscene when we finish. :)