Map<String, Account> accountMap = new Map<String, Account>(); // accountMap: clientCode ---> Account
for(Account clientAccount :
    [SELECT Id, Client_Code__c
     FROM Account
     WHERE RecordType.Name = 'Client']
){
    accountMap.put(clientAccount.Client_Code__c, clientAccount);
}

List<Tax_Payment__c> taxPaymentList = [SELECT Id, Amount__c, Payment_Date__c
                                       FROM Tax_Payment__c
                                       WHERE Payment_Date__c = THIS_FISCAL_QUARTER];
Map<Date, List<Tax_Payment__c>> taxPaymentMap = new Map<Date, List<Tax_Payment__c>>();
    // taxPaymentMap: paymentDate ---> List<TaxPayment>
for(Tax_Payment__c taxPayment :taxPaymentList){
    List<Tax_Payment__c> tempTaxPaymentList = taxPaymentMap.get(taxPayment.Payment_Date__c);
    if(tempTaxPaymentList == null)
        tempTaxPaymentList = new List<Tax_Payment__c>();
    tempTaxPaymentList.add(taxPayment);
    taxPaymentMap.put(taxPayment.Payment_Date__c, tempTaxPaymentList);
}

public class TaxPaymentExtension{
    public static String DefaultTaxType = 'Federal 941';

    String taxType;
    public List<Tax_Payment__c> taxPaymentList {get;set;}
    public Map<Date, Tax_Payment__c> taxPaymentMap {get;set;}

    public TaxPaymentExtension(){
        this.taxType = ApexPages.currentPage().getParameters().get('taxtype');
        if(String.isBlank(this.taxType))
            this.taxType = TaxPaymentExtension.DefaultTaxType;
        this.taxPaymentList = [SELECT Id, Amount__c, Payment_Date__c
                               FROM Tax_Payment__c
                               WHERE Payment_Date__c = THIS_FISCAL_QUARTER
                               AND Tax_Type__c = :taxtype];
        this.taxPaymentMap = TaxPaymentExtension.getPaymentMap(taxPaymentList);
    }

    public static Map<Date, Tax_Payment__c> getPaymentMap(List<Tax_Payment__c> tpList){
        Map<Date, Tax_Payment__c> returnMap = new Map<Date, List<Tax_Payment__c>>();
            // taxPaymentMap: paymentDate ---> List<TaxPayment>
        for(Tax_Payment__c taxPayment :taxPaymentList){
            List<Tax_Payment__c> tempTaxPaymentList = taxPaymentMap.get(taxPayment.Payment_Date__c);
            if(tempTaxPaymentList == null)
                tempTaxPaymentList = new List<Tax_Payment__c>();
            tempTaxPaymentList.add(taxPayment);
            taxPaymentMap.put(taxPayment.Payment_Date__c, tempTaxPaymentList);
    }
}

!!!! This is all mumbo jumbo.  See Update on 2016-02-17 above. !!!

public List<Case> getCaseList(){
    List<Case> returnList = new List<Case>();
    // ...
    return returnList;
}

public String getActivityFile(Date startDate, Date endDate){
    String returnString = '';
    // ...
    return returnString;
}

public class Data {
    public List<String> nameList {get;set;}
    public Map<String, Decimal> amountMap {get;set;}  // amountMap: name ---> amount
}

public Data getData(){
    Data returnData = new Data();
    // ...
    return returnData;
}

@isTest
public class SpecialCaseExtensionTest{

    public class TestData{
        Account testAccount {get;set;}
        List<Case> caseList {get;set;}

        TestData(){
            // ...
        }

        // Have multiple constructors for multiple scenarios
        TestData(Integer caseCount){
            // ...
        }
    }

    @isTest
    public static void testInstanceMethods(){
        TestData tData = new TestData();

        Test.startTest();

        // ...

        Test.stopTest();
    }

    @isTest
    public static void testStaticMethods(){
        TestData tData = new TestData();

        Test.startTest();

        // ...

        Test.stopTest();
    }
}

@isTest
public class AnotherCaseExtension{

    public TestData{
        SpecialCaseExtensionTest.TestData specialTestData {get;set;}
        List<Account> extraAccountList {get;set;}
        // ...
    }

    @isTest
    public static void testInstanceMethods(){
        TestData tData = new TestData();

        Test.startTest();

        // ...

        Test.stopTest();
    }

    @isTest
    public static void testStaticMethods(){
        SpecialCaseExtensionTest.TestData tData = new SpecialCaseExtensionTest.TestData();
        // All I need is the Special Case Extension Test Data!
        Test.startTest();

        // ...

        Test.stopTest();
    }