I'll have to say - that question was a tough read, but let's see if I got the gist of what you are asking. Basically, you want to know if it makes sense for there to be a new process of evolution which combines the "best" traits of both natural and artificial selection - something that allows organisms to adapt to their environment more quickly - and whether this can be caused by genetic manipulation. I am going to go ahead and leave the later parts of the question about limb regeneration etc out for now: you'll see why in a bit.
First, a quick recap on how evolution works. It is, at its core, a process of a species responding to external stimuli and pressures. If the stimuli is natural, you get natural selection, if it is man-made, you have artificial selection. The names of either process do not, in any way, indicate superiority. In fact, it is not strictly correct to say that an evolved organism is "superior" to its less evolved counterpart - it is only better equipped to survive in its current environment.
To bring this back to your question, any evolution that takes place in the absence of intelligent intervention has to be natural selection by definition. We are not going to discuss artificial selection any further.
About the speed of evolution - how "useful" this is to the species really depends on how quickly their environment is changing. As such, evolving rapidly does not make sense if the environment is not changing. You can have all the manipulated genes you want, but if the ecosystem stays static for ten millenia, no evolution is going to happen. If changes are gradual, evolution cannot be rapid.
In a nutshell, the question you posed is not valid for a number of reasons. If you must have such a mechanism for your plot/ world setting, I suggest that you keep away from "evolution" and just have science monsters or something.