Hi Tracy
Firstly Im sure that you are aware parsnip seed dosent last long so I buy a new batch each year to ensure germination.
Secondly there is a ‘halfway’ to growing in pots and that is to ‘chit’ them on a damp kitchen towel then when they are showing signs of growth plant out.
Also some fellow allotment holders had a similar problem and took the thinnings from other people. Im a bit sceptical as to this working but they appear to be confident that it has worked before.