The coil should have recommended installation instructions and how to handle this situation. Given that you have stated there is limited space. A small transition probably will not make any difference. It's like an upflow furnace and coil that do not match. You do not build a transition for that, but there are instructions that deal with the manufacturer's recommended way to handle this. The coil might be shifted to the left or right. The same with the horizontal. It might hang a little low or sit a little high. Just do as the instructions say and all should be well.
if u cant make a quick 6" transition for that on site with some flat stock and a bar folder, come on now..