What about a Tippman M4? They're pretty new so I'd wait on more reviews and things but they are really easy to adapt to a HPA set up from CO2 magazines.
The accessibility to a HPA conversion is the defining feature but if you want it to be a proper project build I guess that isn't the same.
In terms of GBBRs, GHK are really good. They do M4s for ~£450, WE GBBR M4s are around the £275-£320 range.
KWA seem to be out of stock everywhere and judging by the number of retailers who had them...I'd say there was never many imported or much demand?
Correct me if I'm wrong but basically good luck finding a new LM4 anyway.
There's supposed to be a Tokyo Marui GBBR M4 coming out, the MWS. It was announced the same time as the M&P and 870 Breacher but haven't heard anything on it since.