If you want a 6" chef's knife, you should buy a 6" chef's knife. But the reason you give is based on a very common misunderstanding.
With few exceptions a short knife won't do any of the chopping tasks (plank, stick, dice) on small vegetables any better than a medium length knife (240mm - 270mm). When it comes to chopping, the advantage to shorter knives is that they are easier to "point" intuitively, and get the knife aligned with the product so you can make the parallel cuts which are necessary for producing the classic shapes and sizes. However, you can point a medium length knife just as easily if you have a good grip -- including a straight wrist -- and not only get much better production and longer edge retention, but a more natural action from the knife as well.
Furthermore, very short chef's knives are almost all belly. That makes it difficult to get much of a flat section on the board, which leads to incomplete "accordion" cuts; makes it hard to get the point down to the board (scoring shallots for instance); and makes for a lot of handle pumping.
That you can't do light chopping work with a 150mm without mashing your knuckles on the board also indicates problems with your grip. If your already using a pinch to chop (and I presume you are), you need to "come over the top" more.
There are two things really good about a pinch. The first is keeping your knuckles on the side of the handle, and not on the bottom, so they never hit the board. The second, is that a pinch grip makes pointing a longer knife intuitive. If you're not getting the benefits of both things, there's something wrong. In any case, you might try reading Getting a Grip on a Good Pinch
as food for thought if nothing else.
As it happens, I have a 7" Sabatier "Nogent" chef's knife which I bought to break down smallish fish, and like a lot. Because it's a fun knife, I invent other reasons to use it; but I don't kid myself that it's as good a knife for any chopping task -- including small veg -- than any of my (four, 245mm to 270mm) "go-to gyuto." If I were still cooking professionally, I'd use it even less.
If your intention in purchasing a new knife is to get something you'll use more than for occasional, "specialist" work: Think twice, and twice again about a 6" gyuto.
There are a lot of really good gyuto and petty knives running around. The places to start narrowing down the selection is by considering your budget, and what you're willing to do to keep your new knives sharp.
The more you know about knives the better you'll understand why: Friends don't let friends buy Shun