Davidt
AFAIK there is no general mechanical reason why a particular engine should not be run LOP. Any such advice is likely based on the standard plane having inadequate engine instrumentation to make it feasible or safe.
LOP, or even peak EGT, may not be achievable in practice if the fuel flow to the cylinders (or, to be more precise, the power developed by the individual cylinders) is badly matched. The result is excessive engine vibration.
I gather that most carb engines can't do LOP for the above reason, while most injected engines can, to varying degrees depending how well the injectors are matched up. Some people are lucky, most not.
GAMI will take your EDM700 data (you have to run a special flight test, details on their website) and sell you a set of injectors which are designed to make *your* engine balanced.
I don't have GAMIs but do fly LOP routinely at 45% to 65% power; what GAMIs would give me is the ability to run LOP at say 75% power. Reports from other GAMI owners suggest you get a smoother engine anyway. Cost about US$800 plus fitting.
There are reports of additional small fuel savings resulting probably from operation with a wide open throttle (e.g. at 8000ft, 65% power) which means the engine can suck the air in more easily.