I got it all working! Thank you for your code - just needed to readjust.
I am not using the 'RelatedPageID' => 'Int', because I am not trying to form a connection as much as setting a name into the Page table.
I believe I am making a connection with "DivertURLTwo" and "URLSegment" between Page and Sitetree. Not sure if that is ok, but the URLSegment is unique I believe.
Then my code...
function getCMSFields() {
$fields = parent::getCMSFields();
$fields->addFieldToTab("Root.Content.Stratagem", new TreeDropdownField('DivertURLTwo', 'Select the page...', 'SiteTree', 'URLSegment', 'MenuTitle'));
This shows the MenuTitle in the dropdown once saved and puts the URLSegment into the cookie, and calls the right page upon returning to the site page.
I do understand that if the user changes the name of the page prior to a visitor returning that they will receive an error page.
So, again, thank you
Steve