Problem areas:
1) The Zoom is not exactly intended for this use. It's a portable field recorder. I've worked with the H4N several times, and believe me, it's a somewhat decent unit for interview work and such, but it's definitely not a Duet quality-wise for the purpose of tracking guitars.
2) You're using a completely different guitar with completely different pickups compared to what Ola is using. I don't mean it's a bad thing, not at all, but they
will sound different. Ibbys are often described as rather bright-sounding.
3) Most of Ola's tone comes from his playing technique. Seriously. The man is an animal. I might be wrong here, but judging purely from the DI, it sounds like you aren't really digging into the strings with the pick. Good picking technique is crucial for a tight metal tone.
Solutions:
1) Grab a decent interface with a decent instrument input. Sell the Zoom or keep it for other uses. They're easy to get rid of if needed.
2) Either switch to a different guitar/pup-combo or learn to love the tone of your axe as it is.
3) Practice, practice, practice and practice, or alternatively, forget about practicing and dive into the absurd madness of endless gear purchases wondering why the tone is never quite what it could be.
That would be $89.99, thank you!