Ok, spoke to two attorneys, and we now have the reason why the OSG appealed.
OSG: They just don't think that my Minnie would be insane enough not to be suitable for marriage. Damn, I agree. Surprising, isn't it? Stupid law. No, not stupid - criminal. :P
ATT1: Inexperienced, but nice. Referred me to ATT2 who is more senior. Thinks it's a punt.
ATT2: Says we have a good chance if things are presented right. Fee 1.5k for both.
We'll have another consultation with ATT2, this time with both of us. I don't mind the fee if the application is successful, but I am not sure if we do indeed have good chances. Should we go for it, then we'd do it with a lawyer, though - don't want to go any unnecessary risk.