I have had a few smokes in which the smoke reaction (smoke ring) was not nearly as prominent as I would normally get. The only explanation I had for these cases was that I started the smoke at higher temps than I normally would have due to time constraints. Lesson learned there was that you can't rush a good smoke.
Here's a few things I have experimented with over the past 2 years which have effected smoke reaction for me:
By starting the smoke for a butt, brisket or other large cuts at 175-180* for the first 45-60 minutes, then bumping temps up into the 230-240* range to finish, I can increase the smoke reaction by keeping the exterior of the meat from heating up too quickly. Meat takes on smoke much more easily at lower temps, then as the meat temps increase, smoke penetration will slow to a halt. Intact whole muscle meats, cured meats, or smaller cuts are the only pieces I will use this method for due to the danger zone guidelines for non-intact whole muscle meats.
Also, something you may want to try just for the experience is a cold smoke & sear for smaller cuts like chops, steaks, chicken pieces, and even fish. Begin with nothing but smoke (little to no heat) for anywhere from 15 minutes to more than an hour depending on the cut and species of meat, poultry or fish. The flesh will slowly begin to warm through, and as you sear over a hot grill, you can finish it to your personal preferences. If you try this you will notice a smoke ring on beef steaks, pork steaks or chops, and in the bare (skinless) meats of poultry. I've used this method for nearly 2 years as a way to get some smoke after work in the evening or anytime I didn't have all day to commit to a nice long smoke.
There are other factors which effect the smoke reaction as well, and as mentioned above, electric smokers fall in dead-last when it comes to a smoke ring, surpassed by propane or gas fired, but none can develop a smoke ring quite like a solid fuel fired smoker. Smoke reaction is not just created by the smoke wood itself, and I have proven this by cooking on a grill with indirect heat and low temps, or in a smoker with low temps, and in either case no smoke wood(s) were used. I still had a generous "smoke ring" in the meats. The smoke itself will flavor the meats, while a hot/clean burning fire simply supplies the meat with the heat it needs to cook properly. The cleaner burning fuels like gas or propane will not develop the smoke ring quite as well as a less clean burning fuel such as a charcoal fired smoker or grill. It's the oxides in the burnt fuel's gases which create the majority of the smoke ring, and the "dirtier" the burn and lower the cooking chamber temps, the more likely there will be a prominent reaction with the meat.
You should be able to develop a nice smoke ring with a steady smoke from an electric heated smoker, but if the smoke is not there to support the effort, it will likely give less than satisfactory results.
But again, starting lower and working up to higher temps has never failed me in the past, either with propane or charcoal fired smokers, but I would not recommend this with injected, boneless or otherwise tampered-with meats (non-intact whole muscle). I think if you can get enough heat and air to your smoke wood when you first start it up is the key, but keeping it under control as you increase smoke chamber temps will be the next step. I'm not familiar at all with the internals of the MES, but getting the correct amount of heat and air to the smoke wood is the key when using chips or chunks. Also, the smaller the chips, the less heat and air they need to produce smoke.
Lastly, I never soak smoke woods, as it only delays the onset of actual smoke.
Hope that helps you understand the smoke ring a bit more. As for getting that MES to produce an acceptable amount of smoke for the duration, its all about the heat/air getting to the smoke wood...that's as basic as I can explain it. Your smoke woods in a gas or electric rig should be charred lumps after the smoke is finished...that's a good indication of a slow, smoldering, incomplete burn which produces a nice continuous thin smoke.
Stay with it, brother, 'cause when you get it figured out it, your methods will reward you with the best smoked foods which money can't buy.