I think the OP is in the UK so 350,000 yen is over £3000 when customs fees are taken into account. In the UK for that price you could buy a good papered katana so I don't think it would be a particularly wise purchase.
Yes some look good but the odds of getting them cheap are pretty slim. London auctions are well attended by dealers with deep pockets that are happy to pay over the odds for things.
They are quite common in the UK, this one looks pretty reasonable too:
http://www.henrykrank.com/mfsr126.html
and other decent one here:
http://www.michaeldlong.net/kolist45/1/0/500499.htm
You need to check the terms of your insurance policy as sometimes they only cover a fixed amount eg. up to £5,000 when they are outside of your house. You can get specialist insurance policies but the prices are sky high.
Ideally you would need to get them valued by a dealer and have a written appraisal for each sword.
Sounds like you would be better off getting the ferry in future!
I think a best case scenario is shin-shinto. The nakago has clearly been hammered into its current shape and really is a horrid looking thing. I did wonder if it might have been in a Kyu-gunto or cane mount. I guess you would need to see it in hand to be sure, and the awful polish doesn't help, but I thought it looked like some gendaito I've seen in the past.