Perhaps I didn't explain myself correctly. Mauchly's test indicates if
the correlations among the repeated measures are similar (the so
called sphericity assumption). If Mauchly's test is significant
because the correlations are different, then you must adjust the
degrees of freedom using G-G epsilon. But, sometimes (in heavy tailed
distributions) Mauchly's test can be significant even with similar
correlations. Heavy tails are NOT the cause of a failure in
sphericity, but the cause of a FALSE POSITIVE Mauchly's test. In that
case (Mauchly's test significant & very heavy tailed distributions
-outliers present-) you might consider that the sphericity condition
is OK and avoid the use of epsilon correction for the DF.
I'm not really fond of mathematical transformations (you loose contact
with your data in the same degree you gain normality). I remember that
high kurtosis could be prevented by taking two measures, instead of
one, and averaging them. This must be done during data recollection
(has to be foresighted in the designing steps), it can't be done right
now with your data.
Square root or logarithms might eliminate part of the kurtosis, but
the are more indicated for positively skewed data. If your data are
symmetric, then these transformations could add negative skewness to
your problems, but, as the saying goes "the taste of the pudding is in
the eating". Try them and see what happens with your data.
HTH
Marta