Here is what I ended up doing and it works pretty well. I created a sheet, added the necessary code and then saved that code in another module in the project. When I create the new sheet I copy all the code from the module into the worksheets code module. The code is below.
Sub InsertCodeIntoWorksheet(ByRef DesignSheet As Worksheet)
Dim StringLine As String
Dim LineCount As Integer
LineCount = ThisWorkbook.VBProject.VBComponents("NewDesignSheetCode").CodeModule.CountOfLines
StringLine = ThisWorkbook.VBProject.VBComponents("NewDesignSheetCode").CodeModule.Lines(1, LineCount)
ThisWorkbook.VBProject.VBComponents(DesignSheet.CodeName).CodeModule.InsertLines 1, StringLine
LineCount is the number of lines of code in the module holding the code for the new worksheet. "NewDesignSheetCode" is the name of the module holding the code. StringLine is a string that holds all the lines of code. It ends up being a really easy solution but it took me forever to find. I hope this ends up being useful for some other poor person who needs to be able to do this.