I've just completed a Khitomer Space Elite that took nearly an hour (a player left very early on in the game). At the end, right as Donatra's Scimiter was defeated, I died and had to respawn. Upon respawning, all of my team had warped out and I was left to search for the reward drop in one of the larger, more vast STF maps. I spent all of the 120 seconds left searching for the reward drop, but with absolutely no luck.

Is there any other way to do the drop? Maybe use the overflow inventory, because I would hate to miss out on 960 dilithium and 100 Omega marks again.

If you didn't find it at the exact place where you died, it wasn't there at all. There is a bug where if you are dead while a stf finishes, you don't receive the loot drop. Pretty common apparently.

there's another one where if you die when the bonus marks are handed out you don't get them