How can I tighten a large nut under the sink?
The basin wrench you linked to would be the right tool if the hex nut was 1" or less. For a larger nut like this, it was designed to be either hand tightened, or with a wrench like the channel lock or adjustable wrench you linked to. But to use the wrench, you would need to first remove the sink from the counter.

Some newer faucets have worked around this problem by using a hand tightened nut that has two screws on either side. Once you tightened the nut as far as you can by hand, you tighten the screws which press against a washer, firmly holding down the fixture. If you can't get a basin wrench on it, and don't want to remove your sink from the counter, then I'd recommend taking this fixture back and finding one that would be easier to install in your situation.