Please try a few more things:
1. Change the contact behavior to "asymmetric", and set the container as the target and the spring as the contact.
2. May not be necessary, but change the detection method in contact as "normal-to-normal target"
3. Don't use a contact normal stiffness factor larger than 1, for a flimsy container, it better be between 0.01 and 0.1, because the large out-of-plane force will make it hard to converge.
4. Try "augmented Lagrange formulation" for the contact.
5. Don't use a contact damping factor more than 0.1 as it will bring unrealistic behavior to the model. Moreover, since you have already defined "adjust to touch", I don't think you will need a large contact damping fact. Try starting with a very small value, like 0.005.
Please let me know if these works.