To me that sounds better than reckless, but it all depends on the interviewer's perception and how the jurisdiction defines "careless driving".

Reckless is what you get after you try to evade the cops on your GSX-1000 at 0200 on sunday morning, but it turns out you were sober after all when they catch you.

If it were me...

I would get the legal definition from that jurisdiction. Then I would submit the app and additionally send a letter to the interviewers at the airlines you are applying to explaining the difference between reckless and careless...bend over backwards to accept full responsibility though.

Also you still have a few too many recent tickets in my opinion but it does not hurt to apply anyway.