Tom, I installed my Lofrans Cayman, the one smaller than the Tigress, in 2005. I followed the instructions and it has worked flawlessly ever since. The solonoid is wired directly under the windlass---that is the arrangement of the anchor locker, not by brilliance, and to clear-up the jumble of wire, I used a fused buss bar to wire each of the foot switches. This allowed one primary wire and a wire from each foot button. In my case, for the windlass, I used 00 wire and the run was from the anchor locker to the circuit breaker and back---approximatly, 60 feet. A larger wire would have been difficult to work with and the room required to route them through bulkheads etc. would have complicated the installtion. So far, the 00 wire as worked well and I haven't noticed any heat coming from them. To my thinking, the 2.0 wire you mentioned, is too small.
Good luck, you have a nice piece of gear.
Mike Meier