Another way of getting the results:
SELECT x.PackageID, d.ServerName MissingServer
  FROM @DeploymentServers d
 CROSS APPLY(SELECT DISTINCT p.PackageID
               FROM @PackageServers p
 ...

Or something even simpler like this should work:
DECLARE @Cols NVARCHAR(MAX)=''
SELECT @Cols +=QUOTENAME(c.column_name)+', '
  FROM INFORMATION_SCHEMA.columns c
 WHERE c.TABLE_NAME='MYTABLENAME'
   AND c.TABLE_SCHEMA='dbo'
 ORDER BY c.ORDINAL_POSITION

What indexes have you got on dbo.MyTable? I think different index usage between the queries is the problem as you are stopping parameter sniffing by setting the dates within the...

I don't think your query will do what you want. It's selecting the same results in the recursive part of the query that its selecting in the anchor part.
It...

Could you just create a staging table on your data warehouse with the same structure as the table on the other server. Import the rows you need into the staging...

The only way I know is to script all the stored procedures and add the line "with encryption"
I'd create a script for each stored procedure like this:
[code...

You should put the birthdays with their id in a table. Then your query will work.
Also, you don't need the last two lines at the end of your query:

You just need to add the table in a CROSS APPLY or OUTER APPLY and select TOP(1) with an ORDER BY date DESC
...
From Beaufort.dbo.DPIB010 t1
CROSS...

frederico is right, you should change the table definition to store date type values. But you can order that string in date order
SELECT TOP(1) *
  FROM...