The open loop gain of the transistor is actually Rload/Re. Re is .026/Ie. Ie, for a beta of 100, is about 8.72mA. This makes Re=3, and Avol=157. However...
You forgot about Rin which is approx. Re*Hfe, or about 300 ohms. This is significant. I'll let you do the math, but below is the transistor amp and the equivalent circuit. The gain of both is 2.3 in simulation. With a 2N3904 in the same circuit, I also got a gain of 3.35. The higher beta lowers the collector voltage, increasing Ie and reducing Re. This increases Avol, which helps a little in this case, but Rin increases by a factor of 2 or more, which helps a lot.