How to render this, russicorum militum mortes, into English?
Skipping the obvious, the most controversial variants are: Russian-soldier death/s, Russian soldiers death/s.
I don’t really know what is meant by “the obvious” or why the translations you proposed would be “the most controversial”. The common English translations of the Latin phrase - did you make it up yourself? - are the following:
the deaths of the Russian soldiers
the Russian soldiers’ deaths
The article “the” is optional, of course.