Does that mean that you bypassed the normal brake housing you have used under the bar tape and the inline adjuster?
If so, then that is probably a fairly definitive acid test. The only thing which I expect that it would not eliminate as a cause is if the compressionless cable outers do not have clean cut ends, i.e. if either end is ragged/has wire strands protruding there will be compression at that point when the lever is pulled.
If not, and all your experimentation has involved the inline adjuster and normal brake outer under the bar tape, I would suspect them. A short length of ordinary brake outer will not compress much, but again if the ends of the cable outer are badly cut/ragged that might well be a factor.
Similarly the cable outers not being fully inserted into the levers might give exactly the braking problem you describe. I have experienced this when I have stupidly tried to move the levers down the bars slightly without undoing the bar tape: the tape prevents the cable outer moving, and so moving the lever downwards results in the outer no longer being properly inserted in the lever, with resulting poor braking performance. Hence now I always just tape the cables to the bars with a couple of sections of electrical tape to begin with. If I decide to move the levers up or down even just slightly, I usually find it is necessary to remove the electrical tape to allow the cable outers to be re-secured to the bars. Only after riding the bike for some time and when I am completely satisfied with the position of the levers and braking, do I fit the handlebar tape.
Lastly I would also check the instructions for the lever, e.g. do they specify a particular route for the cable entering the lever or that a (particular sized) ferrule must be used on the end of the outer?
