My only other alternative is to add create 60 fact rows for each existing row, which creates its own set of problems...
It's not clear to me why you'd do this, unless you mean in another fact table that would then of course have a different level of granularity. My sole caution is that the correct level of granularity for a fact table is crucial. If you don't have a clear grain and then violate it, your cube will produce incorrect data in certain cases.