Let's say the dipole presents an input impedance of 50 ohms. The 55' of 600 ohm line is just about 90 degrees and will transform this down to 4 ohms...

I think you divided instead of multiplied. Or vice versa...

If the SWR is 12 : 1 on the 600 ohm line (as it would be with a 50 ohm load), the

impedance at the end of a quarter wave section would be 12 * 600 = 7200 ohms

rather than 50 / 12 = 4 ohms.

Which would indeed be a better match using a 4 : 1 balun, but still a rather high

SWR for coax feed.

If you are trying to solve the problem of how to feed a 132' wire when your coax

isn't long enough to reach and you have to use a quarter wave of 600 ohm line,

then you could try a Zepp feed or a Delta Match (which can match 600 ohms, and

a 4 : 1 balun at the base would give a 3 : 1 SWR on the coax.) Both approaches

would still have a high SWR on the coax on most other HF bands.