Well all mine have had free range eggs and I've been feeding them all eggs for 22 years and quite a variety of breeds and the only time I've had any problem was with a hard boiled egg because as you discovered whew the smell !
The only problem with eggs is Egg white contains the protein avidin which inactivates biotin, but egg yolks contain so much biotin that the biotin binding process of the white is not significant. If you are concerned feed yolks only, or soft boil the whole egg.
Not all eggs contain salmonella - get them from a good free range source and they are perfectly safe (even make my own mayonaisse and never had a problem).