Invalid default value for DateTime when changing to utf8_general_ci
This looks like more of a SQL mode issue than the char set. Strict mode (and more specifically  NO_ZERO_DATE which is part of strict mode) usually sets off that error if the table was created with an all zero default date before turning on strict.

What we use (for similar modified date columns), is the '1970-01-01 00:00:01'.

and on a slightly related note, we use timestamp for these columns (and for created time too). Takes half the storage space, and is faster access.