I understand the western Norwegian dialects (/ nynorsk) have a much stronger old / west norse influence so are closer to Icelandic, maybe you are from those regions or are familiar with these dialects?

I'm from the east, but Nynorsk is required for all students (each region picks the main written language they want to use in schools, but also need to teach the other one), so we do certainly all get some exposure to Nynorsk as well and it certainly might help.