Can you link a source saying the -5C4 engines were only available on the A340-300E? The -5C2, -5C3, and -5C4 engines were all options on prior versions of the A340 going as far back as 1995. For example, 9K-ANB is an A340-313 (-313 in the suffix denoting the -5C4 engine) was delivered in March of 1995. The first -313E was delivered as ZS-SXA in 2003.
MTOW was also optionable by the airline, and while it's harder to find data on the specific MTOW of specific airframes, the Type certificate data sheet for the A340 specifies that the maximum takeoff mass of the A340-313 is 276.5t.