First let me point out the real error in the sentences above – you must put a comma after 2003, no matter what.
Restrictive clause – provides information essential to the meaning of the sentence
Non-restrictive clause – provides information, but if removed, would not change the meaning of the sentence
There are those who say that that should only be used for restrictive clauses and that which should only be used for non-restrictive clauses.
There are those who say you could use either, so long as you set off non-restrictive clauses with a comma.
In this case, your adjectival clause is a non-restrictive clause – in other words, when you remove the clause, it doesn’t change the meaning of the sentence. Going by the first rule (which I prefer), you should use which.
The Oxford Guide to English Usage spends quite a bit of time explaining that, while not hard and fast, there are a number of rules governing that vs which.
In your example, the pertinent rule seems to be
So, in your example, I think which is appropriate, because the second clause adds further information to the first clause.
That said, the section on which vs that is about 3 pages long with rules, counter-rules and times when rules can be bent or broken.
I’m in the UK and standard practice here may differ from standard practice in the States and elsewhere.
Use ‘which’ as a relative pronoun in a clause which provides further information about something you have mentioned in the antecedent clause.
Use ‘that’ to introduce an adjectival phrase, i.e. one serving to distinguish a given noun or noun phrase from others. In ‘The house that jack built’, ‘that Jack built’ is an adjectival phrase distinguishing one particular house from others. It serves the same role as an adjective such as ‘red’ or ‘big’.
‘That’ can also be a conjunction, serving to link or associate two ideas or clauses.
But Xerxes is right - the so-called rules are impenetrably foggy and ‘experts’ can argue back and forth for hours to no great effect. As with most things pertaining to so-called ‘correct’ use of language, what matters above all is that your meaning is clear and unambiguous.