If there are no (of insufficient) statistics available, either don't allow auto-resolve, or don't use the statistics to determine it.
Here's my issue: I love sniper rifles. I'm pretty sure I'm losing these missions because the game's valuation of them doesn't take into account how well I use them; that is, it just thinks "These are game-start gear, and so aren't up to par with mid/late game missions.". Maybe I'm wrong, but that's going to happen.
The idea behind taking statistics into account isn't to replace the classic designer-set valuation method - it's to adjust it. If I, as a player, suck or rock at using this or that equipment, have the game notice - the idea is that the auto-resolve resolves it as if *I* played the mission. I mean, how often have you been surprised by how a player uses or does a certain thing; how effective this or that is in their hands? Don't try to predict the effectiveness of everything ahead of time - take the data the player is giving you, and use that.
I don't see how your abuse case works, and I don't see how it's any less abusable than it is now. I save before every mission (takes about a second and a half, esc-save-click-enter-esc-continue), and if it goes really poorly, I just reload. Bam, ensure a win. If you mean, retry until whatever random element is in there gives me the number I need to win - any system with randomness has that issue, and, to be frank, I'm not suggesting any. I think you should have some, but it's not inherent to this strategy.
The generalized rule of game design I'm working off of is to never *require* a player to do a something they consistently succeed at. If they enjoy it, by all means, let them repeat to the end of time, but when they stop enjoying it? Don't require them to. When I've curb-stomped the same aliens (or near enough) on the same map for the fifth time, don't make me do it again. And if the auto-resolve thinks I'll lose, when I have always won, you're effectively making me do it again, or not at all.
TLDR: Take all those things you're talking about into account - soldier skills, equipment, and a bit of randomness, and then adjust based on how well that formula would have predicted the battles I've already fought. So let's say every time I walk into battle with what the formula thinks is winning, I lose, and every time I walk in with something it things should lose, I win, it should flip it's expectations. Make sense?