Bit curious - there may be underlying problems not mentioned.

re: it is not instant file initialization enabled - very few cases where this should not be enabled -...

just to make it clearer
Publisher
------> Distributor
---------------> subscriber 1
---------------> subscriber 2
---------------> ....
---------------> subscriber N

the above can be any server - they could...

why not just convert the date to a string on the source select - converting to a format that SSIS knows well will then make the conversion to date straightforward. 

Using a linked server can also be done through synonyms - so they do fall under the same as a hard-coded db other than the code that is referencing them.

A few comments on your code.

Do not as a standard store user functions on master  -- master.dbo.ufnStringToPbase  should be on any db other than system db's
Do not...

I do think you took the wrong approach there unless you didn't tell us of further steps that would normally be required.
But by your list of steps I...

the .net version of SQL Server has nothing to do with what your code does. Unless its a CLR, and even that I think it will still allow it.

by the error you posted it seems you tried to use a format that is not possible
Create failed for Login '.\TestAccount'.
drop that .\ and it will work