After working on this for a few hours, I have found a way to fix it. There are two parts to the problem:
1) The forum software gets it's timestamp from two different places. The forum time comes from the Apache server and the posting time stamp comes from the SQL server
2) The hosting company has these two servers out of sync by one hour. I tried a different server within the same hosting company and that one was out by 15 minutes. Third time lucky, the third SQL server had the same time as the Apache server. So I worked around the problem by migrating the forum to the third server.

After some google search, I discovered that this problem is not unusual with hosting companies. I really like the forum software, but perhaps one suggestion for improvement would be to get the forum time from the same server as the database. Then if the database server has the wrong time, it's just a matter of changing the offset in the forum configuration options.

Anyway - it's great software and a massive improvement on what I was using before, so thanks.