Only something along the commitment of the 0.5-1hr "weed out" question can/should be done remotely.
If you're going to require people to do ~7 hrs of tests, that had better be at the office, pairing, with other folks (and at least give them a free breakfast/lunch/dinner!). 7 hrs while working a 40hr (or more!) week is a pretty hefty commitment, and I see no reason why that should be solely the burden of the candidate.
You should be able to trust one or two short, simple weed-out conversations (I tend to do one 30 minute "deal-breaker" discussion on non-tech stuff {make sure their and our deal-breakers are met}, then one about 1hr tech screen {fizzbuzz-sorts of things, but more diagnostic}).
After that, you should have a general sense of whether or not they are a) smart and b) can get stuff done. From there, you need to take a risk and bring them in. What is proposed is not fair to the candidate.