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If your structure has symmetry and all of your ports are located on and centered on the axis of symmetry, you can use the symmetry feature in Sonnet. It should save you a factor of 4 for memory and around a factor of 8 for simulation time.
I think they can handle one axis of symmetry, which is essentially a magnetic wall. If your circuit has an electric plane symmetry as well, you might be able to use a wall of the PEC bounding box to create an electric symmetry plane. But that is only if you don't have ports on that side of the circuit, I think.
No, you can't use symmetry for this case, unless you're interested in common-mode S-parameters alone (which is what you would get if you used the box symmetry/H-plane symmetry feature in Sonnet).
For full general S-parameters, you need to simulate the full structure.
If you have Sonnet Professional, you could use Conformal Mesh, which really speeds up inductor simulations and other simulations with transmission lines that have high memory requirements. It can be combined with Sonnet's thick metal simulation to create pretty efficient inductor analysis.
Have you tried sending your file to Sonnet Tech Support? I had a pretty complex multi-layer coil which I thought was too complicated for Sonnet too, but then I contacted their support guys and they taught me how to be more efficient. So my suggestion would be to send your Sonent project file to support. Sonnet is more accurate than HFSS for planar coils, so it should be worth it.