I don't think they take that much creative license.
What do you mean by authentic?
Most of their pieces are very accurate and they do copy original parts when they can. I know. I myself have lent them parts. I've advised them on several occasions.
LE, SE, and AP are all the same prop version. These would be the most accurate usually.
EE is idealized, made from "better" materials
CE is made from cheaper materials
They will never be better than a replica made from the same real parts as the original, but they are the best replicas made from scratch.
Price -
Who is cheaper?
Parks? for the Graflex and MPP. Yes, he is. The MR replicas are more solidly put together (permanently attached grips and bubble strip).
Most detailed, finished fan made sabers will cost about the same as an MR.
All of the above are as accurate or more accurate than the best fan made replicas too.
Fan made ROTJ Luke sabers might be cheaper since the are relatively simple, the the MR's are still very accurate.
The MR Obi ANH is probably the least accurate, though probably still cheaper than buying all the fan made parts to built it yourself.
Had MR continued with SW I'm sure we would have seen a retooled Obi ANH Elite.