Since the first solution didn't seem to work, I'll have to revert my changes and go for an update via the adapter instead. Here's what I've done:

• Dropped my manually created Code Metrics table in the TfsWarehouse database:

USE [TfsWarehouse]
GO
IF  EXISTS (SELECT * FROM sys.foreign_keys WHERE object_id = OBJECT_ID(N'[dbo].[FK_Code Metrics_Build_Build_ID]')
AND parent_object_id = OBJECT_ID(N'[dbo].[Code Metrics]'))
ALTER TABLE [dbo].[Code Metrics] DROP CONSTRAINT [FK_Code Metrics_Build_Build_ID]
GO
USE [TfsWarehouse]
GO
/****** Object:  Table [dbo].[Code Metrics]    Script Date: 12/06/2007 05:53:00 ******/
IF  EXISTS (SELECT * FROM sys.objects WHERE object_id = OBJECT_ID(N'[dbo].[Code Metrics]') AND type in (N'U'))
DROP TABLE [dbo].[Code Metrics]

• Returning warehouseschema.xml to its original state (i.e. copy the backed up version and replacing the new with the old one, or you could manually just delete the <Fact>...</Fact> added before)
• Run SetupWarehouse again, just in case:

C:\Program Files\Microsoft Visual Studio 2008 Team Foundation Server\Tools>SetupWarehouse -rebuild -v -o -s ORCASBETA2_TFSV -d TfsWarehouse -c warehouseschema.xml -a ORCASBETA2_TFSV\TFSSERVICE -ra ORCASBETA2_TFSV\TFSREPORT -mturl http://orcasbeta2_tfsv:8080 -l log.txt
SetupWarehouse: Warehouse updated successfully.

• Navigate to the warehouse web service and perform the Run command again.
• Verifying in Microsoft Excel that the cube and the perspectives still are there, intact.