I agree with the other posters on this subject. In Alaska, if a guest stays for 7 days or more, they can claim residency in your unit and hosts might have to take the guest to eviction court. I wouldn't chance it.
It's better to accept a bunch of one-day reservations to build up your listing and obtain reviews.
It's a little rude for this guest to demand that you lower your rate by $50+ per day. I understand it's for a long term stay, but that isn't a fair request.
Also, what if the guest doesn't work out for you for whatever reason? Then you'll be stuck with them.