Updating Editor and Modified for a publishing page

Question

I'm trying to update a publishing page in SharePoint 2010 with new Editor and Modified values, but the ones I pass (that I copy from another page) are not saved.

I've tried Update(), SystemUpdate(), UpdateOverwriteVersion() - nothing works. Is there a secret trick? I've tried the suggestions in other similar questions but the situations are a bit different.

Code snippet below:

...
$page = $web.Lists["Pages"].GetItemByUniqueId($uid)
$page["Editor"] = $e      # user from another page
$page["Modified"] = $m    # date from another page
$page.SystemUpdate($false)

Answer 1

This simple example works for me:

$web = Get-SPWeb 'http://aissp2013'
$list = $web.Lists["Pages"]
$page = $list.GetItemById(4)
$user = $web.EnsureUser('contoso\aaronp')
$page["Editor"] = $user   
$page["Modified"] = '11/14/2014' 
$page.SystemUpdate()

Answer 2

Five years ago I created a custom field type to support changing those props from the UI. I've based my solution on the code sample found here:

SPListItem item = ...; 
item["Created By"] = web.EnsureUser("luisb").ID; 
item["Modified By"] = item["Modified By"]; 
item["Created"] = DateTime.Now.AddYears(-3); 
item["Modified"] = DateTime.Parse("01/01/2000"); 
item.UpdateOverwriteVersion();

As you can see, it utilizes the UpdateOverwriteVersion method, and not the Update / SystemUpdate methods.