Not as bad as you might think. It's a variation of the XM204 *soft recoil* type gun mount. Of which there's also a 155mm version, though the projectiles are larger, and fewer could be carried aboard an aircraft. The 105 is likely the way to go, even if the larger gun could be so mounted.
Interestingly, there was a concept a couple of years back to mount a pair of XM204s on either side, aboard a CH47C *$hi!hook* [officially, Chinook helicopter. Don't know how well flight firing tests for that one worked out, but it's interesting to see that the Army has been thinking of alternate possibilities just in case the USAF decides to drop the A10 altogether.
If memory serves, the 105mm howitzer they use is an M102 light towed, demounted from its usual home.