I am trying to insert Account/Contact/Customer records into SFDC using Rest API. i have written the following class. I am able to create the Accounts and Contacts, but I'm having issues creating Customer records. In my setup, Customer is  a child of Contacts, and Contacts a child of Accounts. How should I rewrite my class and JSON to insert Customer records along with Contacts and Accounts in a single call?
Apex Class:

@RestResource(urlMapping='/test/*')
global with sharing class OrderWebServices{

@HttpPost
   global static void createSomething(Wrapper1 test){
		  
		 Account obj = new Account();
		 obj.Name = test.name;
		 obj.AccountNumber = test.accountnumber;
		 obj.External_Id__c = test.externalid;
		 insert obj;
		 List<Contact> conList = new List<Contact>();
		 
		 for(Wrapper2 con : test.Wrapper2){
				  Contact obj2 = new Contact();
				  obj2.LastName = con.lastname;
				  obj2.Email = con.email;
				  obj2.AccountId = obj.Id;
				  conList.add(obj2);
		 }
		 insert conList;
		//Below doesn't insert related Customer
		List<Customer__c> csList = new List<Customer__c>();
		for(Wrapper3 cs : test.Wrapper2){
				  Customer__c obj3 = new Customer__c();
				  obj3.LastName__c = cs.lastname;
				  obj3.Email__c = cs.email;
				  obj3.AccoountId = obj.Id;
				  csList.add(obj2);
		 }
		 insert csList;		 
	}
	global with sharing class Wrapper1{
	  public String name{get;set;}
	  public String accountnumber{get;set;}
	  public List<Wrapper2> Wrapper2{get;set;}
	}
	global with sharing class Wrapper2{
	 public String lastname{get;set;}
	 public String email{get;set;}
	public List<Wrapper3> Wrapper3{get;set;}//Add this for Customer object?
	}
	global with sharing class Wrapper3{
	 public String lastname{get;set;}
	 public String email{get;set;}
	}

}

Here's the JSON payload:

{
	"test": {
		"name": "Test Acc",
		"accountnumber": "12345",
		"externalid": "12345",
		"Wrapper2": [{
			"lastnmame": "last",
			"email": "test123@test.com",			
			"Wrapper3": [{
				"lastname": "customer",
				"email": "customer123@test.com"
			}]			
		},
		{
			"lastnmame": "last2",
			"email": "test456@test.com",			
			"Wrapper3": [{
				"lastname": "customer2",
				"email": "customer123@test.com"
			}]			
		}]
	}
}

The Account record and Contact records are inserted, but the associated Customer__c records are not inserted. I have an external id field 'External_Id__c' which ties all three records, even though Contact is a child of Accounts, and Customer__c is a child of Contacts.

How can I revise the class to be able to insert multiple contacts and multiple Customer__c records?

Thank you!