It’s not that there’s no storage capacity left, it’s that if you have May contracts you are going to pay a big premium to store oil in Cushing as capacity decreases in future months. The discount reflects the storage cost premium.
If you have an old oil field that is at end of life, couldn't you pick this stuff up at $-40.00/barrel and pump it back into the empty reservoirs? I'm sure there is regulation against it, but if it was once a production reservoir, why couldn't you store it there? You would have to drill. You wouldn't have to do much at all.
You would need a suitable formation in terms of geological properties and then you'd need to drill and complete an injector and a producer well. Best case, you would probably lose half the stuff you're trying to store due to multiphase flow in reservoirs being a total drag. Worst case, the oil you're storing isn't compatible solubility-wise with the residual oil left in the reservoir, and you cause massive asphaltene precipitation and lose your entire storage well.