Smoke ring is one thing, and smoke flavor another.
The article posted by Diva did a little to explain how smoke rings are formed. It may help to know a little more. The ring is caused the presence of three things. 1) Nitrogen compounds like nitrates and nitrites; Myoglobin (explained in Diva's article); and bacteria.
The bacteria occur naturally in meat, but in cut meat they concentrate on the surface because that's where the air is. Their diet consists of a narrow range of proteins, including myoglobin. In the presence of nitites/nitrates the chemistry changes so that when the bacteria break down the myoglobin the residue turns purple. These organisms are most active at temperatures between 80 and 120 F. If heat build up is slow enough, and enough of the other conditions of life are present, the bacteria will reproce and thrive below the surface of the meat as well. By 140 they're all dead.
Slow burning wood produces a number of chemical artifacts, including the relevant nitrogen compounds. The compounds and slow heat build up trigger the bacteria to reproduce below the surface and to make the purple color we call the smoke ring. However, the bacteria can fix nitrite/nitrate from other sources -- like liquid "cures." (Judges are instructed to ignore the ring because it's so easy to produce artificially.)
You can probably get the deepest penetration of ring by creating conditions favorable to the bacteria. The conditoins are: Meat with a damp exterior, but marinade not too acid. Surface temperature not too cool, but interior cool -- say half hour out of the refrigerator. But producing a consistent, deep smoke ring is not certain.
Over smoking is another problem altogether. A lot of it has to do with the size and shape of your firebox. I don't understand the actual dynamics, and have never heard anyone claim to on anything above the "informed speculation" level. If you've got a giant offset with a huge firebox you can burn straight green wood, hulls, bark, wet wood, all day long and no problem. If you've got a small bullet or small offset, it's a good idea to choose your smoke wood carefully, and stop burning smoke wood roughly half way through the cook to avoid acridity.
Rules of Thumb (who the hell was Thumb?): The smaller the cooker, the less smoke. The stronger the wood (mesquite for instance), the less you use. The more problematic (bark for instance) the less you use.
We also hit another problem and that's cooking at too low a temperature. Setting aside "cold smoking" which is a different process altogether -- you can't really cook meat at a chamber temperature below 210. We all know stuff happens, and temps sometimes spiral out of control sometimes. The more time you spend below that, the more problems you make for yourself. Here, the extra time required to cook made for overexposure to smoke. Also, the wood was burning at that low temperature where it throws off the highest proportion of unpleasant compounds. Not good. AND there are food safety issues.
If you have a particular fire building method and know the ramp up from 180 to 225 is quick and certain, you might want to take advantage of the lower temperatures to jolt the smoke ring bacteria. Why not?
Rich