If it existed, it would be in the Gameplay.constants file in the
C:\Program Files\Stardock Games\Sins of a Solar Empire - Trinity\Diplomacy\GameInfo
directory, under the section playerDiplomacyAIDef, but I don't see any variables there which would affect mission times.
I did test out changing "questTimeoutRatio 0.5" from its default, but I saw no change in mission times.
a mission was impossible given the situation and the failure set my standing back to the point where the one alliance I was building collapsed
The AI isn't very good at missions, or at diplomacy in general, unfortunately...
You did fully upgrade the basic relationship research, and you also maxed out the relationship gain through donations of credits/resources, and trade agreements, right? If you do all that, you should (normally) be able to get a cease-fire, at which point you can send envoy ships, and after maybe 10 minutes you'll be certain to stay on good relations with that player.
and so did the game in short order.
Military loss? Simple (but very cheap) solution. Build fully upgraded starbases on your front lines. The AI will suicide its fleet on it, every time. (But make sure to have a few fighters on hand to take out enemy torpedo cruisers)
I can't say I'd mind if someone pointed out the existence of a means to fiddle the mission standing rewards too.
Yes, there is, I just tested out changing "missionHappinessModifier 10.0" from its default. The higher the value, the more relationship standing is gained/lost for each mission success/loss/
You can also try changing some of the other variables there if you want, they might help whatever you're trying to do.
If the AI is being stupid with missions and diplomacy, I might offer you to try playing multiplayer, where the strategy gets much more interesting, and where rote memorization of tactics doesn't guarantee a win.