I think I would run the gutter around the corner past the valley. Then on the outside edge, add a piece of flashing that sticks up 6 or 8" so that the bigger flow coming down the valley doesn't overshoot the gutter.
If your are going to put the downspout right there anyway, the conductor head looks like a very good option, and might not need to have a flange of flashing sticking up if it is installed so that the line of water coming off the valley hits the far edge rather than going over it.
The bigger issue I see with extending the roof to 34" isn't support...you could always add a knee brace or something to support it. No, being in PA I think a large roof overhang like that is going to give you a cold section of roof right where all the snowmelt will be coming down. It will hit the colder roof section and freeze and be a constant source of ice dams. Yeah, you could always run heat tape, but I think I'd rather have the shorter roof and then create some form of funky looking gutter. Beats patching roofs and walls from water damage later.