Reading other newspaper reports about the case, the John Reed who was transported was a Sheriff's Officer, or in other words, a Bailiff. There are some earlier newspaper reports about him including one in the Yorkshire Gazette 29 October 1831 which also mentions his wife, Elizabeth. Unfortunately he doesn't sound a very pleasant man.

I've had a quick look for the baptisms of their children and found the following:

24 May 1830, York, St Olave
Charles Benjamin s/o John & Elizabeth Reed of Gillygate, Bailiff

28 Oct 1832, York, St Olave
Joseph s/o John & Elizabeth Reed of Gillygate, Yeoman

26 Feb 1835, York, St Olave
Reuben s/o John & Elizabeth Reed of Gillygate, Sheriff’s Officer

24 Sep 1837, York, St Olave
Mary Ann d/o John & Elizabeth Reed of Gillygate, Sheriff’s Officer
Born 02 Sep 1837

Unfortunately I didn't find James or Richard, but it was only a very quick search.

So if I have the right family in 1841 & 1851 then the above baptisms do seem to indicate that the John Reed who was transported was the father of Joseph Reed.

The age of the John on your tree is still inconsistent with the age of the John who was transported though so possibly needs some further research.