What can I do to avoid a page from inheriting the master page conditionally at run time?

You can attach a master page dynamically to a content page. Because the master page and content page are merged during the initialization stage of page processing, a master page must be assigned before then. Typically, you assign a master page dynamically during the PreInit stage.

void Page_PreInit(Object sender, EventArgs e)
{
    this.MasterPageFile = "~/MyMaster.master";
}

Please note this article on MSDN:

http://msdn.microsoft.com/en-us/library/c8y19k6h.aspx

Thanks,
-RG