The F-35 general arrangement is very similar to one of GD's LWF/ADF proposed layouts (Upper left here). In fact, if it won instead of the F-16 arrangement we know today, the F-35 might be considered a "silent eagle" LO version! (Although since it's much fatter it would only passingly resemble it and in reality be a completely different aircraft, kind of like Superhornet vs Hornet)
Quick reference comparison between F-35A and F-16C Block 50 (quick wiki)
F-35A Length/Wingspan: 15.67m / 10.7m
F-16C Length/Wingspan: 15.06m / 9.96m
F-35 Empty Weight: 29,000 lbs
F-16C Empty Weight: 18,900 lbs
F-35 Internal Fuel: 18,498 lbs
F-16C Internal Fuel: 7,000 lbs
F-35 Thrust (Dry/AB): 28,000 lbf / 43,000 lbf
F-16C Thrust (Dry/AB): 17,155 lbf / 28,600 lbf
The F-35 is nearly the same length and span, but carries ~2.5 times the internal fuel (plus room for ordnance) making it very thick and ~10,000 pounds heavier empty, completely negating the advantage of the significantly better engine. This is akin to the military obtaining new lightweight gear to shave 10 pounds off a soldier's load, only to go ahead and add 11 pounds worth of other crap. It's little wonder it's a dog, but it's defended by those saying it's system oriented rather than performance oriented (like the F-22). The US can get away with this and just say the F-22 will always support operations, but some nations are intending to use these as their primary combat aircraft, so it would be nice if it could perform.
IMO, a more conservative approach with a reduced internal fuel load requirement of 11,000 lbs (equivalent to F-16C with CFT, plus 10% to help offset the difference in SFC) would allow for a lighter (even when considering the naval requirements) less draggy airframe, and if you kept the 2D thrust vectoring of the F119 when designing the derivative you'd end up with an aircraft that can deliver 2x PGMs like the F-35, but generally outfight other 4 / 4.5 gen aircraft. You'd be a bit heavier empty than an F-16 with CFTs, but would be cleaner and have a much better T:W. The end result would be better instantaneous turn rate / nose pointing (with the ability to more rapidly regain lost energy), as well as superior sustained turn rate.
To compensate for the reduction of internal fuel, plan for LO drop-tank assemblies under the wings as options (2x 4,000 lbs or so) that, when jettisoned, takes the pylons with it. This would surpass the F-35A's internal fuel, but likely not much extra range since the arrangement is draggier.
I found a picture with a rough idea of what this could look like (guess from some video game fantasy...)
Keep EOTS as a combined IRST / targeting pod, but get rid of the rest of the DAS and revolutionary systems (KISS), just a basic matured HMD.