First, let me say I've only made through about the first 20 posts in this thread, plus the above post, so my apologies if what I say here has already been stated.

In the form above, the magnitudes of Ia, Ib, and Ic are unbounded. Let me restate the problem to be sure I've understood it correctly. Ia, Ib, and Ic are the coil currents, consider them to be complex numbers (in polar form, if you like, comprising a magnitude and a phase angle). The above equations are just:

|Ia - Ib| = 256

|Ib - Ic| = 294

|Ic - Ia| = 341

Here | | is the magnitude operator on complex numbers. So all the equations are saying is that the three points Ia, Ib, and Ic form a triangle in the complex plane with sides of length 256, 294, 341. That triangle could be anywhere in the plane, so individually Ia, Ib, and Ic could have arbitrary magnitude.

Basically, given any solution, you could add an arbitrary (complex) value to Ia, Ib, and Ic, and you have another solution. If I understand correctly, that would correspond physically to saying that there could be an arbitrary circulating current in the delta coils that would never show up in the line currents as it cancels out of each pairwise difference.

If there is some physics that says this won't happen the problem may be tractable. For example, suppose the physics says further Ia + Ib + Ic = 0 (as complex numbers). Now the translational degrees of freedom have been removed, and the triangle must be centered about the origin. There is still a rotational degree of freedom present, but that is just a convention about phase angle, so we can arbitrarily set Ia to be purely real. This leaves just two possible solutions which are mirror images of each other. If we arbitrarily insist that Im Ib > 0, then there is only one solution, which we can compute.

Since I have no idea if the requirement that Ia + Ib + Ic = 0 is supported by the physics, I won't proceed with the computation.

Cheers, Wayne