This exact problem happened to a friend of mine last year.
His car wasn't a 57 Buick it was a 60's chrysler but the symptom was the same.
He had to replace a fuse for the wipers when it blew and tried to do so at night time so he could drive the car home in the rain.
He pulled the blown fuse and replaced it with a good one while straining to see under torch light. He then started the car.......wipers worked fine and off he went home. Got home and tried to turn the car off and it would not turn off no matter what he did

in the end I think he had to disconect the battery.
I won't go into the full story of what he did to the cat to try to rectify the problem but he spent a lot of time and head scratching wondering what the heck was wrong

He decided to retrace his steps starting with the fuse box and found that the new fuse was sitting wrongly in the fuse box.
Instead of being in it's correct position it was sitting in between the wiper fuse position and another(I'm guessing ignition?) and so it was effectively hot wiring the car so that once it was turned on it was preventing it from turning off.
I don't know the layout of a 57 fuse box or if the same scenario is possible but the stories are so similar I thought I would share his story just in case that may be your problem.
Before you go pulling everything apart and attacking starters etc have a look at the positioning of the fuses to ensure no crossover has happened.
As my friend said in the end.............it's most always the simple things that cause the problem and very often they are overlooked because we think something more dramtic has happened.
Hope you have success