Agree on all counts apart from unbalanced; I think they are already too penalized.
It's pretty much impossible to feint well with them (yes, I can feint with them but not quickly enough for them to be very hard to block, they just surprise people for the first few times) and pretty well every time I try to feint but it doesn't work, I will appear to feint but will actually swing.
I think there should be grades of unbalance, ranging from impossible to stop your swing once it starts to being able to stop it until almost the very end. Also, I think there needs to be some incentive to use them. Generally they are horrid for dueling which is kind of silly, I would personally love to use an unbalanced looking weapon but none of them work. Maybe they could give some additional slow when people are hit by them or if they block them, so that they are better for kicking/nudging or something like that.
In M:BG I very much think combat should be more bash (aka nudge) based which would allow large weapons to be usable in 1v1 situations. At the moment they are only effective if you sneak up on people or are supporting/supported by others. Or unless you are fighting against someone that sucks, but I don't think that's very reasonable for the weapon to be good vs crap people.
Regardless, the 2nd part MUST be fixed.
Also, I may well be wrong but I would have thought a sword would be significantly more heavy than an axe in real life. Seeing that the sword is completely metal and the metal not being very good at the time, you couldn't make them very thin so there would be quite a lot. Compare this to an axe which has a relatively very small piece of metal atop a substantially lighter wood handle, and I would've thought the axe would be more powerful, lighter (thus maybe faster?) but less wieldy than a sword