Hi Gaston,
I sympathise, but there are two factors against you here. Fares for late adopting NR lines (like GN) are generally higher than comparable tube and NR lines which use TfL prices. This is a historical issue but there doesn’t seem to be any political will to synchronise fares. Then there is the second issue which is the premium added when you use the late adopting NR lines along with tube or DLR. Again this is historical, although it does only affect fares when the journey involves zone 1.
You are correct that up to Finsbury Park there is no difference because that part of GN has always charged tube fares, largely because you can’t tell which way someone has travelled. There is also the small matter that Finsbury Park is in zone 2 so I would expect the fares to be cheaper than to Harringay in zone 3.
If you want to try and understand how things work then take a look at the Fares Guide page.