The Surly fixer does not fix the cassette body, you remove the cassette body and replace it with the Surly Fixer, which has threads for a cog and lockring. Meaning you would still have the same chainline issues.

The options I can think of are:
You can put a spacer on your drive side BB cup to push the chainring further away from the bike.
You can put spacers on the rear hub to push the chainline either way.
You can put spacers on the chainring bolts to move the chainline away from the crank (Either direction depending on if it's on the inside or outside of the spider).
And you can replace the BB.