Peabody appeared on the island with one other person and the winter spiders he didn’t travel by boat, that means a Way or teleportation, the winter spiders were accosting wizards travelling the Ways, so that is the logical method. Someone high up in Winter was trying to isolate the WC from Chicago. Peabody was photographed coming out of the waypoint in Chicago, no explanation is give as to how he got from there to the Island, but we know a viable route existed from Chicago to Arctis Tor and therefore Maeve. Peabody just needed to get across town to Pell’s. It would be handy if he had an ally resident in Chicago to drop him off on Pell’s Nameless would be ideal, especially if this were his/Cowls long term plan to install Peabody as Warden.
Basically this was Cowls/Nameless long-term plan, one of the reasons he first associated with Kemmler, and then sought Asylum in Winter. Peabody was his mole in the WC working to become Warden and access the lore of the inmates, Maeve ran interference on the Ways through Winter to Chicago and got Peabody to the Island because nemfected.