Thanks for that. I’ve now worked it all out.
Firstly, the £3.75 is the railcard discounted off-peak incomplete journey which was charged because you touched out at 0930. Before 0927 it would be the full adult incomplete journey.
Now, the main problem is actually not down to the EOSI, but instead it’s the continuation exit marker on the validators in the subway. As I mentioned, the validators are part of the Underground station, which doesn’t matter normally, but does cause an issue in this case. Continuation exit works within the maximum journey time from the origin station. Weekdays, that is 100 minutes for a zone 5 to zone 2 journey. So, your touch in at platforms 7/8 is 90 minutes after the touch in at New Barnet and platforms 7/8 are part of the National Rail station so the system treats your journey as continuing. By the time you get back to New Barnet you’ve long exceeded the 30 minutes allowed for a here-to-here journey so it charges an incomplete journey instead.
So, to stop this happening you need to first touch in on the validators by platforms 1/2. As this is the same station as you exited the continuation exit marker will expire after 15 minutes, but with the EOSI you need to leave 30 minutes. You can still touch in on the gates to platforms 7/8 if you need to because the continuation entry setting will allow that.
I’m going to pass this over to my contact at TfL to see if anything else can be done, but in the meantime I’d be grateful to know whether touching the validator first does cure the problem.