What do you do if your API calls a SOAP Internal and you get back a response  SOAP Client Classes generated from WSDL . 

You have to change those classes to extend %JSON.Adaptor,  Would have been nice not to change generated classes. 
For this reason it would be nice to be able to use %ZEN.Auxiliary.jsonProvider or then a replacement .

Or is there any other way of handling this?

Sorry what I meant to say was  is that I removed compiled and saved the storage that was created on compile time. We always keep the storage in tact in the class , Fully aware of the storage importance
Then tried to run load on zpm and still got the error

This is a new development and we do know that after it has been deployed you should not delete storage else it can cause issues