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@lae
You might have 4 different rear cogs, but like I explained above, they're all roughly the same size. The lowest freewheel gear (i.e. your hill gear) is only 12" lower than your highest fixed (i.e. your flat road) gear. I personally wouldn't consider that to be enough.
You'd need long dropouts to do it too. And it assumes that the chainline from the outermost chainring to the innermost cog won't cause issues, even with a 3/32 chain it's a big jump for a fixed gear.