Thanks for all the great information, guys!
I bought the handles a couple years ago so I will check and make sure I have new gaskets.
So you think I have a decent chance of getting the screws out, with penetrating oil? They have been in there for 57 years, so I am not taking anything for granted. If I have to drill the heads off, it won't be the end of the world.
But in general, you have given me lots of optimism that this is a reasonable job. Lubing all the mechanisms in the meantime is a bonus.
Since we are in the process of getting 18" of snow, it doesn't look like I will be driving the ol' girl anytime soon, so I can patiently get into this.