[SalesForce] How to use this VF page in another VF page

Not something I can test locally, but some things I changed looking at it:

I use a Set to keep track of all possible names before querying, to filter out duplicates. I calculated the arrays of names once and stored those arrays in an array of the same length and indices as the trigger.new array. (We've found that pre-allocating arrays of known length doesn't make much different to CPU governor usage, especially here as the array is no bigger than 200).

Set<String> allSubAccountNames = new Set<String>();
List<List<String>> subAccountNamesByOverview = new List<List<String>>;

for (Contract_Overview__c newCont : Trigger.New) 
{
   String[] subAccountNames = splitField(newCont.Subsidiaries_On_Contract__c);
   allSubAccountNames.addAll(subAccountNames);
   subAccountNamesByOverview.add(subAccountNames);
}

Map<String, Id> subAccIdsByName=new Map<String, Id>();
for (SubsidiariesAndBrands__c subAcc : [select id, Name from SubsidiariesAndBrands__c where Name in :allSubAccountNames]) 
{
   subAccIdsByName.put(subAcc.Name, subAcc.id);
}

My split function is

private String[] splitField(String value)
{
   value = value.replaceAll('\[|\]','');
   return value.split(',');
}

It may be possible to do this in a single REGEX, but we become more obtuse.

The other main difference is I did an insert not an upsert at the end as they're new records.

List<Subs_Serviced_On_Contract__c> subs = new List<Subs_Serviced_On_Contract__c>();
for (Integer i = 0; i < Trigger.New.size(); i++) 
{
    Contract_Overview__c newContract = Trigger.New[i];
    String[] subAccountNames = subAccountNamesByOverview[i];

    for(String subName : subAccountNames)
    {
        Id subId = subAccIdsByName.get(subName);
        System.assert(subId != null, 'Failed to find subaccount by name ' + subName);

        Subs_Serviced_On_Contract__c ssoc = new Subs_Serviced_On_Contract__c(
            Name = subName,
            Contract_Overview__c = newContract.Id,
            Account__c = newContract.Account__c
            Subsidiaries_and_Brands__c = subId,  
            Contract_and_Sub__c = newContract.Name + '~' + subName,
            Contract_Start_Date__c = newContract.Contract_Start_Date__c,
            Contract_End_Date__c = newContract.Contract_End_Date__c, 
            Logo_Usage_Allowed__c = 'Yes');

        subs.add(ssoc);
    }
}
insert subs;

I have had the same problem. The solution was to use tha native html select list and an visualforce hidden field. After each change on the selectlist the currently selected value is saved to the hidden field:

<!-- Here is the native select list. 
     It is empty, we fill it later with own options.
     Notice, that by onchange the selected value will be send to the hidden field. -->
<select id="someList" onchange="jQuery('[id$=selectedItemHidden]').val(jQuery(this).val());">
</select>

<!-- Hidden field with a reference to the apex variable -->
<apex:inputHidden value="{!selectedAccount}" id="selectedItemHidden"/>

<!-- Here we fill the select list with some options -->
<script>
for(var i = 0; i < optionsArray.length; i++)
{
    var opt = new Option(optionsArray[i],optionsArray[i]);
    jQuery("select#someList").append(opt);
}
<script>

You can pre fill the html select list with options from the database:

Controller:

public class MyClass{
    // Here we define the list with accounts
    public List<Account> accounts { get; set; }

    // In constructor we will read the accounts
    public MyClass(){
        accounts = [ Select Id, Name From Account Limit 10 ];
    }
}

Page:

<!-- Here we just use repeat function to iterate the list -->
<select id="someList">
    <apex:repeat value="{!accounts}" var="a">
        <option value="{!a.id}">{!a.name}</option>
    </apex:repeat>
</select>