You could go with your original idea of venting through the back of the house if you get a suitable fan, rather than the basic bathroom type.
ATC, for example, do a range of centrifugal fans which are suitable for long duct runs. You can read the brochure [broken link removed].
They have a technical support line, the number is on their website. They won't sell you the fan direct, you'll have to go through your electrician, but they'll advise you what size of fan and ducting you will need.
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