Squares rather than hexes gives you your 45 degree turns, boresight can be worked out of you've passed through the position of an adrift ship or a ship that has already moved. Arcs and ranges are easily worked out as is movement (some rounding likely depending on square size)- the diagonal question I would take a leaf out of Peter Pigs rulesets and say the first costs normal, thereafter double. Hotz Mats do a 2" square grid which I was hoping to pick up - been a bit slow tho :-(.
Measuring can be an issue, and these models have a habit of falling over or getting otherwise knocked - a grid of some kind reduces replacement imperfections and removes the need for a ruler to hover over someone's beautifully painted ships.