Upsizing the downspout is heading in the wrong direction. You have virtually no lineal footage of gutter in that small corner, and very little possibility that you are overloading the capacity of a standard leader. I had one fairly small neighborhood where I had about two dozens new homes built. One Saturday evening, it rained about nine inches in a few hours. It was a disaster. Roads washed out, new ditches in yards, crawl spaces filled with water and flowing out of the vents. At no point did a customer report that they had gutters overflowing, since the downspout was full. In some cases we are talking gutters 20-25' long, with roofs no smaller than yours. A gravity feed 2x3 will discharge at least 120 gallons a minute. I doubt you are anywhere near that volume. In a good rainstorm 120 GPM, confined to a tight discharge area, even for a few minutes, will leave one hell of an erosion ditch. Think fire hose volume here. Not to beat a dead horse, but I've done this for a living, forever it seems, and you might want to take a look at my list of potential issues to address. Say you invest the time and money on a bigger leader, (which I have yet to see on a single family residence, ever BTW). Now it rains, and you have water flowing over the top for one of the many reasons that, I and other knowledgeable folks, have addressed, What's next? Remember, typically the outlet that transitions to the leader is a round neck fitting that drops into a 2-1/2" hole. If you leave that in place, putting a larger leader on is a total waste, since the current outlet will restrict the flow severely. Now you need to cut most of the bottom of the gutter out and install a 3"x4" outlet, with less than a 1/4" to spare on the flat area of the bottom of the gutter. Tough for an experienced metal worker, and unless you remove the whole thing, you are doing it upside down. Doesn't matter who chimes in here, with what advice, until you are outside, in a rain storm and looking at why your gutter is not functioning, it doesn't matter if you change leaders, regrade the yard, of hire a witch doctor to dance in the driveway, it won't help. You can't fix a problem if you haven't identified what that problem is.
If, during a biblical deluge, you determine that the gutter is filled to the top, and the downspout if full, then rehang the gutter dead level, and add another 2x3 to the other end. A 3x4 is a pretty big piece, doesn't transition well to 5" K gutter, and will look like ass, IMHO.