5-string TI flats on a 4-string Jazz bass?
 

Will the first 4 strings of a JF345 set (G,D,A,E) fit a 4-string Jazz bass? My concern is the E. I don't own a J bass, so just going by pics, there's seems to be little room between the nut and the tuning peg for the E.

Yes, the E string in the JF345 is the same JF34100 string found in the 4 string JF344 set.

The JF34100 string is 37" long, the winding should come up to the side of the E string tuning post.