I have only limited experience with gratuitous Space Battles (didn't find it particularly to my liking) but have been playing the Dominions games for ages (and there is another, similar game from the same people called Conquest of Elysium which is along the same lines combat-wise). Could you be more specific about how there is "a lot of input besides the customization"? Do you mean there are too many options for the army?
There are some tangential examples I can think of where the player has only limited control over fighting. The Majesty series (of which the first was superior in my opinion) puts you in charge of a kingdom where all you can do is bribe heroes to do this or that, but you have no direct control over their decision making in or out of combat. In the Paradox grand Strategy games like Crusader Kings, Europa Universalis, and Hearts of Iron the player assembles armies and throw them at other armies, but has no directly control over tactics or whatnot.
I'm referring primarily to the scope of the game. It is a huge game.
The example I was looking it fits more the 'mini-game' definition though it has quite a lot of breadth considering this classification.
The game is really just that, a sandbox environment where you tweak your army with no limitations of time or resources beyond a static points cap and the content you've unlocked in the game, and sequenced battles (either as survival waves or specific level armies to beat).
It is almost just a puzzle game where the fun comes from configuring an army from content you 'own'.
Gratuitous Space Battles does something similar where each win earns you resources to spend on new content, which further increases your ability to outfit a custom army to field. It is simple and efficient and isn't encumbered by a larger system. Though I didn't love GSB, I felt it was a decent game especially for its price, but I'm looking for something more streamlined and more importantly, readable.