Here is a quote from a former Boeing Technical Fellow for Aerodynamics that I got after emailing them about this very topic. I thought the community might be interested in his answer.
From the mid-90's to the mid-2000's, significant advances were made in
computer-based tools for closed-loop aero shape optimization,
Multi-Disciplinary-Optimization (MDO) tools for doing complex
multi-dimensional trade studies across scores of design variables,
structural Finite Element Analysis (FEA) optimization for structural
weight and stiffness. Much of this work was done as part of attempting
to meet the requirements of the HSCT (High Speed Civil Transport)
through its NASA-funded "HSR" element, and the follow-on industry
internal R&D efforts toward designing other "concept planes" like the
Sonic Cruiser, SSBJ concepts, and Blended-Wing-Body (BWB). The
supersonic airliner concepts and SSBJ in particular, required being
able to optimize not just the wing shape, but the wing, body, and
nacelle shapes simultaneously, optimizing to find the best possible
compromise between cruise aerodynamics, transonic acceleration,
subsonic cruise, and low-noise takeoff and landing performance. The
very thin, supersonic wings and tails, also provided significant
weight reduction, aeroelastics, and flutter challenges that acted as
catalysts for the improved structures tools. The MDO capability (still
evolving) helped make the right kinds of trade-offs, i.e. "optimum
compromises", in the design of the 787 and 777X. The improved CFD for
air-loads prediction were coupled with FEA strength and stiffness
optimization and these were used to guide direct optimization of
aerodynamic shapes. The advent of practical direct CFD optimization
of detailed aerodynamic shapes for 787 enabled the computer to find
multiple incremental drag reductions that the "pressure matching"
methods used on the original 777 could not. This optimization plus
the development of very strong carbon fiber primary wing structures
resulted in trade-offs that determined it was better to make the wing
thinner while using less sweep to get a fairly high cruise Mach of
0.85--- the resulting thinner all-carbon wing was plenty strong enough in bending, but was more flexible than previous wings.
It's not a total answer, and I wouldn't expect anyone from Boeing to give one, but nevertheless, it definitely confirms that a shift in design tools away from inverse design and towards direct lift/drag optimization led to incremental L/D gains.
I inquired a bit more about what specific flow features the optimizer was finding, and he said:
Very generally, yes, the computer-driven optimizations would seek ways
to improve L/D not just drag or drag-rise. So they don't really use
pressure distributions per-se as the figure of merit, rather the
actual L/D that results from various shape changes. This means that in
addition to trying to further reduce shock strength, they try to
incrementally raise the net difference between upper and lower surface
pressures thereby creating more "L" for a given "D". They also
distribute the lift span-wise in a patter than does not follow the
"ideal" elliptic lift distribution but rather try to create a
down-wash field that allows the horizontal tail and fuselage lift to
"trim" the airplane while minimizing the far down-stream wake. In a 2D
airfoil sense, carrying lift farther aft on the wing (both to increase
L and reduce shock strength) can cause thicker boundary layers,
increasing the parasite "form drag", but the thicker boundary layers
also have less local skin friction--- so the optimizer can seek the
best L/D trade-off of the various drag sources (wave/shock drag+skin
friction+span load induced drag+ tail and wake induced drag + wing
pressure form drag), and of course do this in the presence of the
nacelle and strut. It can also camber the nacelle and strut shapes,
change inlet lip shapes to reduce inlet drag, and put local "blisters"
or waves in wing surface, or change the shape of root fairings or wing
tips to get a better combination of local pressure and the local
surface slopes those pressures act on in the lift and drag directions
(very much a 3D effect !). You say you have trouble picturing what
would be advantageous for a full 3D optimization, but that is exactly
the point--- the computer can systematically do the grunt work to
investigate the effect of thousands of candidate shape variations,
identify which have the most performance leverage, and recommend
specific shaping trends that do not violate multi-disciplinary
constraints (spar thickness for example).
Anyways, hope the community appreciates. Not going to reveal the name of the Fellow, but can confirm privately if needed.