You could try making it wireless rather than put the logging on the gun. Something like an Esp8266 might do it if you buffer the measurements. Also look at the Particle Photon which will do TCP out of the box. Squirt the data to a pi and do the logging on there.

Your problem is that you need to find some asynchronous storage or transmission method. For example in barebones avr, writing to the spi data register initiates a transfer, but you can do other things while you wait ~8 clocks for it to send. Interleaving like this can go quite a long way on 8 bit hardware.

In Arduino, there may be a lot of safety checking and blocking going on. Other chips (eg ARM) can do things like DMA where you can route data from eg a serial port straight into something else.