Timestamp-based index
Changing your table from a heap to having a clustered index should significantly improve your performance on both queries and perhaps even on inserts. Generally speaking, your clustered index should be narrow, unique, and ever increasing. Using a datetime that you can't guarantee to be unique is not ideal because it's 8 bytes and, since it isn't unique, sql will add a four byte uniquifier to non unique rows. You may be better off using an identity column with an int as your clustered index and, since that's what the "row_number" queries are really after anyway (an ever increasing unique number) that might be a great way to go especially if you have a number of nonclustered indexes already (because the clustered is used as a row pointer by the nonclustered so it adds size to them). The 4 billion available int values leave you decades of growth. 

I suggest you make a testing copy of your database and then test it with a clustered index on your datetime value and contrast that with a test using a clustered index on a new identity column (and a nonclustered index on your datetime). See which one does better with your query load. Both scenarios will outperform a heap.