Does anybody have any suggestions in what I can do to improve the pace at which a scan is carried out?
Use a faster scanning system; whether it would work with this particular LIDAR unit is a question, though.
For one thing, the offset of the transmitter and receiver portions of the sensor might make it difficult.
Secondly, the wavelength of the system (905 nm) might make optics cost a bit more than you want.
The fastest way to do the scan would be to use a pair of galvonometers (driven closed-loop) with mirrors attached, so that one scans the X axis, and the other the Y axis.
You could even do this without galvos, if you have some precise-controlled speed motors spinning multi-faceted mirrors - again, arranged in an X/Y scanning fashion (look into how they do it for laser light shows, or for early mechanical TV systems). This kind of a system would be easier to construct, as well as cheaper (as galvos and drive electronics aren't inexpensive). Note that for such a setup, you would need some kind of timing index marker on the spinning mirrors (so you can tell where the mirrors are positioned).
The second fastest way (but more complex in other ways) would be to spin the whole unit - mount it on a turntable rotated by a motor, feed the signals from the sensor thru a 6 pin slip-ring conduction device - and have an index sensor so you know what direction the sensor if facing for each "sweep". You'll only be able to rotate the sensor so fast (10 - 20 rotations per second, most likely), mainly due to limits on the slip ring system (faster speeds are possible - but the slip ring becomes much more expensive).
In effect, this will give you a 360 degree "2D scan" (like a radar - this is basically how the LIDAR sensor on the Neato XV-11/21 vacuum cleaner robot works) - once you have that, you can rotate/tilt the whole spinning affair to scan the other dimension (which will have to be at a much slower rate, due to the gyroscopic effect of the spinning unit). You might be able to do a separate mirror scanning the "Y" direction as well.
Finally, note that all of these scanning methods are going to have distortion (even your pan/tilt system) due to the polar coordinate nature of the scans (which you might have already noticed - and perhaps even corrected for in your software).
Hope this helps, or at least gives you some ideas...