Update: I solved the problem!
First off, I learned that there is more to the measurement of gain than simply measuring the S21. The following link talks about three different gains: transducer power gain, operating power gain and available power gain in the context of LNAs.
http://www.ek.isy.liu.se/courses/tsek03/SpectreRF_LNA533AN.pdfI followed the above link and re-measured the gain. In the process, I discovered that I had made a few changes to the circuit in between measuring the S21 and transient gain! With the version inconsistency removed, I see an agreement between the values of operating power gain and transient gain :)
Note: For those who are looking at the numbers in detail, my design does not have output impedance matching. Therefore the available power gain is negative :o