You might want to re-think your shade needs. Up in Toronto, the amount of sun you get is far less than you would get down in the Caribbean, and every bit of shade helps. While a small bimini might be suitable for the Toronto conditions, you should probably plan the boat to handle the conditions you will see while on your cruise.
Actually, the design would use three 130 W solar panels as the first level of "shade", with awnings deployed front, back and both sides from beneath those panels. I suspect I will have them able to pivot to screen as needed. Think a canvas and SS tube version of a car's windscreen shade...enough to cast a decent shadow on the small working area on deck.
The cockpit itself is tiny: about 60 by 30 inches by 15 inches deep. The deck and the rail "benches" are not typically in use underway if there is any sort of wind as we are moving about working the boat.
If I had a bunch of people aboard for drinks and whatnot, I could easily suspend a white plastic tarp awning, as do the Pardeys, as there are plenty of vertical lashing points. Ideally, I want an arch to be strong enough to be permanently in place, but with the bimini elements to be collapsable or removable in terrible weather. Similarly, I would have the capacity to unmount the solar panels, leaving a stripped arch in place.
But thanks for thinking of my shade needs! Alex's boat, sailing at 37 degrees North close to the summer solstice, with no bimini, was an education. A good hat made all the difference, but I still got burned on the back of my legs because we were travelling SSE all day.