I've looked at the on-line criminal records and there isn't much information at all, but York Reference Library will apparently do a look-up service for the York Assizes records.

York FHS has an index to these records and John is listed as follows:

ID 5795, Reed John age 45 date: 07 July 1838

http://www.yorkfamilyhistory.org.uk/resources/york-assizes/

Im assuming you have the marriage details to Elizabeth North, but just in case:

John Reed of the parish of Alne, farmer & Elizabeth North of the parish of Stillington married at Stillington on 10 April 1822. Witnesses were John Wood & William Silversides.

He was probably the John Reed born 31 Jul 1794 and baptised 24 Nov 1794 at Newton on Ouse, father also John Reed.

ADDED: I see from your tree you have the John Reed who married Elizabeth North as b 1802 Alne. This would fit the marriage information but the age is wrong for the John who was transported.