Why not make it an option: Detailed reports / Simple Reports for in game log presentation?
Detailed is like what you posited; Yasuaki Okamoto's Snap Shot hits Sectoid Soldier for 16..
Simple doesn't reveal as much like you also posited: Yasuaki Okamoto's Snap Shot critically hits Alien.
Of course, I'd have the detailed report also generated and automatically appended to a TXT log file that is attached to that savegame.
If anything else, the text logging would make debugging a lot easier; to find pesky bugs regarding weapons formulae, etc.