I'd come across a map somewhere of the planet Enroth, which showed Antagarich way off to the southeast of Enroth. It's on Artstation, if anyone's interested. Though, I do understand that it's just one artist's rendition, and not the "Official" world of Enroth. Though, the "Official" map of Antagarich shows Emerald Island more east of the Tularean Forest
Looking at Antagarich in the artist's rendition map, I noted a tiny island southeast of Nighon, which looks every bit like Emerald Island to me.
I'd figured easily three weeks from New Sorpigal to Emerald Island, anyway. As for going to Harmondale, looking at said maps, I'd say five days to Pierpont, then two days to Harmondale from there by stagecoach --- as it's four days to Tatalia from Harmondale (Two to Steadwick, two more to Tatalia from there.) Alternatively, it could have been two days to Steadwick, and five (By foot) to Harmondale from there.