Linq2Sql: How to handle tables with the same name and different schema names

Question

I have a database with multiple tables which have the same name but are from different schemas. For example:

[DatabaseName].[Schema1].[MyTable]
[DatabaseName].[Schema2].[MyTable]

When Linq2Sql generates code for this database, it appears to just be picking up the table from the first schema and completely ignoring the second schema:

[Table(Name="[Schema1].MyTable")]
public partial class MyTable {  }

This effectively makes it impossible to query the table on the second schema using Linq2Sql. Is there a workaround for this?

My first idea is to manually edit the generated code so that I have:

[Table(Name="[Schema1].MyTable")]
public partial class Schema1MyTable {  }

[Table(Name="[Schema2].MyTable")]
public partial class Schema2MyTable {  }

but having to maintain this code every time the database changes would be a huge pain. Any other ideas?