Haneda to Narita safest option

Hi,
Have the option to fly home from Osaka airport but as I wanted to stay another day the travel agent said I had to fly from Narita instead, flying from Osaka Itami or Kansai to Haneda or directly to Narita.

The Narita flight arrive about 9.00 and the haneda flight about 7-8.00 if I remember correctly.

My flight back to Europe then leaves at 11.40.

As Haneda is a bit away from Narita I wonder how quick and safe I can get to there without missing the flight from Japan.

There are more flights to Haneda than Narita.

And no I wont go to Tokyo the day before as I dont have time or money to travel by Shinkansen and my Jr pass has ended by then.

From Hyperdia, HND to NRT involves so many train switch and may take 90-130mins.

the bus takes 85mins.
BUT.. im not sure about any road traffic congestion
https://www.limousinebus.co.jp/en/bus_services/narita/haneda.html#time

but honestly, this is really pushing it as you are taking international flight and need to be at airport like 2/3hrs before departure

Pushing it either way, it looks like. Like the above poster said, it is recommended to get to Narita 3 hours before an international flight. Now, it's never taken me 3 hours to get through everything, but stuff happens and safe is better than sorry. I think you should fly to Narita the night before, stay at an airport hotel, then fly out. Otherwise, try to find the earliest Narita flight and at least you'll be there already. Going to Haneda is risky with that tight a schedule however you try to go between the airports.

Hi OP
Any reason why you want to stay in Osaka for another day?
To explore more?special event? do you still need the night to be in Osaka as well?
Alternatively, you can consider night bus Osaka to Tokyo.
http://willerexpress.com
expensive(since you need to fork your own monies), but still cheaper than shinkansen + night accommodation

There are direct trains on Keikyu from Haneda to Narita Airport.
It is not an hour on hour service for the direct trains, time taken is about 92 mins and costs is about Y1800, no Ltd Express surcharge.
The train changes names 4 times , Keikyu, Toei Asakusa , Keisei and finally Keisei Narita Sky Access. For the direct train, the destination signboard will show Narita when the train pulls into the platform , and likely will display Keisei insignia and there is also an overhead platform display showing the trains routing.
From the flight timings you gave, this train is not workable either.
I travelled from Yokohama to Haneda by bus, missed my 1105hrs connecting train thus caught an 1145hrs train arriving Narita 1317hrs to catch a flight departing at 1530hrs.

Have you ever considered Peach air. They have cheap direct flights from KIX to Narita Airport : http://www.flypeach.com/home.aspx