Hi Niall,
Welcome to NMB. In terms of overall shape despite the discolouration, I think this one is in better condition than the other one - the first blade looks like it has had the point re-shaped. My feeling is that this is a later blade than the first and I'd say shinto with again maybe with some Mino influence based on hamon and the file marks on the tang. The tang might have had some after-sales work done on it as it looks a little roughly shaped and the file marks seem a little variable in shape and depth and these points are normally addressed with some care by the smith.
The boshi looks like it might be ichimai meaning that the hardened edge takes up all of the kissaki and might be a kantei point as it is, whilst not exactly rare, a little out of the ordinary.
As regards getting them polished, speaking from the head it probably doesn't make financial sense to do so as you would not recover the money laid out, but they're your babies and there is a Japanese qualified polisher working in Oz so you could at least get them looked at. I suspect the second blade would be the one to have done as the shape of the point on the first one might not leave enough hardened edge to work with.
You could try a little WD40 to loosen the habaki on the first blade, leave it for 24 hours and see if it makes a difference. I don't think it will stain the blade but give it a good wipe over with something soft once you have the habaki off.
Hope that gives you something to go on and that you enjoy your new swords. You'll surely get some more informed comments in a while.
Best,
John