The nearest train station to Hinxton is Whittlesford on the Liverpool Street to Cambridge line... so your third (and possibly best) option would be tube to Liverpool Street, train to Whittlesford, cab from there. There are a couple of cab companies around the Whittlesford area, but I don't believe there is a taxi rank at the (very small) station so you would have to phone for a cab. If you look up Whittlesford station at www.nationalrail.co.uk you will find numbers for a couple of taxi firms.

As for the little quirk you noticed about tube arrival times... I've noticed that myself, I think the train journey planner just works on the basis that "maximum journey time is X" but doesn't check for actual times. If you want actual times for the tube you can always look those up at www.tfl.gov.uk