Here is the PowerShell code to create a webpart page:
Add-PsSnapin Microsoft.SharePoint.PowerShell
$pageTitle = "Page Name"
$layoutTemplate = 4 # Template code
$web = Get-SPWeb http://server/site
$list = $web.GetList("http://server/site/LibraryName/")
$xml = "<?xml version=""1.0"" encoding=""UTF-8""?><Method ID=""0,NewWebPage""><SetList Scope=""Request"">" + $list.ID + "</SetList><SetVar Name=""Cmd"">NewWebPage</SetVar><SetVar Name=""ID"">New</SetVar><SetVar Name=""Type"">WebPartPage</SetVar><SetVar Name=""WebPartPageTemplate"">" + $layoutTemplate + "</SetVar><SetVar Name=""Overwrite"">true</SetVar><SetVar Name=""Title"">" + $pageTitle + "</SetVar></Method>"
$result = $web.ProcessBatchData($xml)
$web.Dispose()
# Possible LayoutTemplate values:
# 1 - Full Page, Vertical
# 2 - Header, Footer, 3 Columns
# 3 - Header, Left Column, Body
# 4 - Header, Right Column, Body
# 5 - Header, Footer, 2 Columns, 4 Rows
# 6 - Header, Footer, 4 Columns, Top Row
# 7 - Left Column, Header, Footer, Top Row, 3 Columns
# 8 - Right Column, Header, Footer, Top Row, 3 Columns
Source:http://social.technet.microsoft.com/Forums/sharepoint/en-US/39c98f27-248c-40b7-b859-088c7dcdeedc/cannot-create-web-part-page-with-powershell?forum=sharepointadminprevious
You can then add the webpart to the webpart page by using the code prsent in one of the posts you mentioned in the question.