Here are a few suggestions for Keith to help resolve his dilemma:
1. Ask his cousin in Australia for as many details as possible about the Nortons who contacted them - full names, approximate ages, locations they/ancestors lived. Every detail could provide a clue.
2. Search records like censuses, BMD indexes, passenger lists for matches between the Norton family in Australia and Keith's known relatives. Look for shared names/locations that indicate a connection.
3. Contact the Norton family directly to exchange family tree information and try to find the point where the trees connect. Collaborating directly often yields the best results.
4. Consider DNA testing if paper trails don't provide conclusive answers.