You're right that sitting for six weeks would be unfair on her, such a small bird has even less reserves than a larger one and shouldn't be asked to lose any more weight. Also, as you're going away you won't be on hand to see how things turn out. It would be best to isolate her in a small grass run or other bare enclosure, cool but open to the light, and prevent her going into anywhere cosy and dark, as this is the best way to break a broody. Light and air will help to reset her hormones so after a few days she will be back to normal. She will run around protesting loudly, but will be getting exercise and feeding up. Also this method is easier for whoever is looking after your birds whilst you're away - she can rejoin the flock after a few days once she stops wanting to go into the nestboxes. She should be kept in a bare box or dog carrier overnight if her bare pen isn't safe from foxes as snuggling in a dark nest box will slow down her recovery to normal. Leaving her out in the pen in the open air is best, in a corner of a secure run if you can manage this, but her safety overnight is more important.
I don't think the cold water method is as useful or natural as exposure to light and air, because exposure will quite rapidly return her hormones to normal without the shock of dunking in cold water, and is much more humane as well. Once back in the flock, she should return to lay after a week or so in recovery, and when she has laid a clutch she may well go broody again and you could give her more eggs at that point, there should still be plenty of summer left for a successful hatch. As you've discovered, it's best to get everything ready in advance and avoid any last- minute changes to the nest and coop - and also, if possible, plan to be around at hatching time!
Good luck and let us know how it goes.