Well even if you take the most symmetric halves by volume, the density of an ideal elephant is not uniform. Some organs don’t come in pairs and all that

I guess it depends on how many hairs you want to split and how precise you want the answer

However most unpaired organs don’t contribute to a mass asymmetry. It’s thought this has evolved to aid with locomotion as any asymmetry will negative impact on efficiency

The answer can never be precise for the very reason that not all elephants weight the same (breed, age etc.).

I was looking for an average from the get-go, but a half is a half!

I agree with you that a reasonable answer is an average, but a half on a volume basis is not necessarily equivalent to a half on a mass basis

I disagree. You can have a left half and right half, but also a front half and rear half.

Half of the weight of an element would be well defined since it is just a number.