Has anyone had success creating distortion through effects without creating feedback or sacrificing volume?
The more you add effects like distortion and overdrive into your sound, the less volume you will get before feedback.
'Overdrivng' can be accomplished by how much airflow goes through the harmonica, how loud and hard you play through a mic (bullet mics tend to overdrive fairly easily which is why they are so popular), overloading the signal going into your amp and/or speakers, or by using special pedals or effects to create a synthetic 'overdrive' sound.
The first and best choice is to create your 'overdriven' sound at the harmonica with good quality, loud breathing technique. Listen to James Cotton's acoustic playing to see what this sounds like.
All in all, the cleaner you keep your electronic sound and signal path the greater volume you will get before feedback. It is then a trade-off as to how much electronic distorted sound you want vs. the final volume you will receive. At rehearsals or on stage, you can always "mic" the amp speaker to help increase your volume to compete with the other instruments.
Work on your breathing and playing technique first, and then research the good mic and amp combos. After that, you can experiment with effects. I, like many players, started out trying every effect on the market, but ultimately worked harder on my playing ability and ended up with a cheap mic and a loud clean amp setup for my "live" sound that allows me compete with the drums and guitar player. Remember, it's better to be heard with a less-than-perfect harmonica sound than it is to have the state-of-the-art harmonica sound that no in the audience can hear above the other instruments.
Here is a post with the info on the equipment that I use for the studio and for live playing-
Listen to CD Song Samples-