John N,
Here are the choices you listed:
A. Install a dual action fuel pump. $80-$100+, especially if you want an original-style glass bowl dual-action fuel pump.
B. Install an electric replacement wiper motor. There are no after-market electric wiper motors that do not interfere with the original radio (unless someone has started making one in the past few years).
C. Don't drive in the rain. Might be an option in some places but would require excellent weather forecasting in IL.
D. Simply just live with it. And, hope for the best.
Or, here are two other options:
E. Find an original 1954 optional electric wiper (RPO 320). These are rare and sell for $150+.
F. Rebuild your [wiper vacuum] pump or have it rebuilt.
If you search in this forum for "fuel pump" [correction: "wiper vacuum pump"] you will find a few threads with advice about reconditioning fuel [correction: wiper vacuum] pumps and/or having it rebuilt ($65). The following company was highly recommended:
Wiperman.com Some people have reported excellent results on having their pump rebuilt.
Tim