Yes, they make chucks that you can dial in. The magic is in the back plate, not the chuck itself. They go by names like "True Set" or "Run True".
BUT...
All the ones that I have seen only allow you to dial in the concentricity, not the angle. The best way that I know for controlling the angle is to mount a back plate on your spindle, being very careful that there are no foreign substances between the back plate and the spindle, and take a light cut with it in place to bring it true to the spindle's rotation. Then, mount a high quality chuck on that "dialed in" back plate.
And again, all the ones that I have seen have four adjustment screws that operate just like the jaw adjustment screws on a four jaw chuck. They do not provide the mounting pressure so they will have a finer thread which allows more precise adjustment. They still have to be loosened and tightened in pairs but the final tenths are often done with just increasing the pressure on one of them. Then, when all is OK, the bolts that hold the chuck to the back plate are tightened. Perhaps you could make one with two screws and two springs. I've never heard of this being done so, if you do, let us know how it works out.
I guess you could add three or four screws that would allow adjustment of the angle, but there probably is no way to eliminate interaction between the various screws and they would probably be more trouble than the added adjustment is worth. Just my opinion.
I have a shop made back plate that does the above with four set screws. It was not difficult to design or make. I did use some spring washers on the six bolts that hold the back plate to the chuck so they stay in contact when those bolts are loosened for adjustment. Here is a photo where you can see two of those four adjustment screws:
Those adjustment screws simply rest against the OD of the chuck.