Actually, you would not get pushed backward. Take a look at Reavers picture. The only way to hold that rifle, if you can lift it at all, is to basically hug it to your chest while leaning over it to put your face into the scope. The second you fired, you'd be sent into a spin, since you cannot make use of the shoulder rest to absorb and DISTRIBUTE any of the recoil. Further, with a max strength of 2, and a tiny body, there's a not insignificant chance of you shattering your arms after you fire it.
actually, no.
the arm in the picture is at full extension, and even then it does not reach the trigger from the butt stock.
Simply put: "Little T-Rex arms don't reach"
At best. you are looking at more of a shoulder mounted, like a WW2 bazooka, or panzershrek(sp?).
Then there is the physics of the torque.
We are talking about a large object being extended out past the center of mass, an object that has considerable weight to the object..
EXAMPLE AT HOME TIME!
Grab the jug of milk from the fridge, hold it close to your chest. Now hold it straight out in front of you. Notice the muscle strain difference, yet the actual weight didn't change?
I don't know the math Torque off the top of my head (its an auto-fill on the program at work

), I'll leave that up to the more arithmetic inclined

But I can give you an example that I do know off the top of my head, just because I deal with it all the time.
An Aerial manlift with a boom extension of 80ft, has a base weight of 56,700 lbs, and at max extension, can only support 500 lbs, anything more and the machine will tip! (and I know this because I have to weight my tools AND gear for the basket every time I use a machine for insurance reasons after 3 tip overs in 15 years.)
But, basically, this would be the Hulk of pixies to pull it off.
Inconnu,
The fact that you are not on the ground makes it WORSE, not better. By being airborne, you take away your own mass as a counter reaction to the recoil. Now all that 18,000 joules of energy is transferred to you to absorb.
This goes back to the laws of Physics. Again. The impact velocity of the weapon into your frame by the recoil, is now resisted by the smallest point, outward, without mass (as in gravity and your weight) compensation. The first thing impacted at 18000 joules of energy is your soft tissue (at point of impact), followed by ligaments (at PoI), Then Bone (at PoI), spreading outward to the rest of your frame, and then finally impacting your change in direction; Which is a factor of speeds and directions of impacts, and all other fancy science things that go beyond the pay grade of an Instrument Mechanic...
In short, that 18000 joules goes INTO you before it changes your direction. And given your mass as a Pixie, That could mean INTO you as in "the rifle stock enters your chest cavity, ending your life instantly".
Again. Pixies and Guns Don't Work.
Lets put this into more real world perspective.
The 51-Mustang, mounted a Merlin RR Engine with an output of 1400 horsepower without Boosting. It was also armed with 6 Browning .50 cal machine guns with a fire rate of 600 rounds a minute.
A 3 second burst from the guns would slow the Mustang 3 to 12 km/h depending on altitude.
The P-51 Mustang had a gross weight of 12,300 lbs.