How can I get my gas fire pit to have a larger flame or better disperse heat?
We had a similar issue.  The solution is to stack up larger chunks of lava rock into something that is vaguely pyramid shaped.  As you note, the heat rises and if you have a large stack of rock over the flames, the rock will redirect this convective heat through the rock and heat up the rock itself.  Once the stack of rock is heated (ours gets quite glowing red in the middle), it radiates the heat out to the sides (where people are sitting) quite effectively... much better than the flat layer of rock in the bottom of the fire pit.  Since most of the heat is in the middle of the ring, that is where you want your stack tallest since it will extract more useful heat that way.  

The only thing you need to be careful of is the stack of rock tumbling down.  Fortunately, lava rock is quite porous and there is a lot of friction between two pieces.  You can easily stack the rock in an interlocking manner and test it but pulling or pushing to ensure that the stack is stable, and that red hot rock won't come tumbling out on you while the fire is going.  With heating and cooling, the rock will shift over time so it is best to inspect the stack periodically to make sure it stays stable.

Note, I'm talking about large size lava rock, not the stuff I see in your fire pit.  Something like what you see here: