The other factor in the demise of the F136 (now acknowledged by GE insiders) was economic. The payoff for a competitive engine would be lower unit costs and lower operating costs (as a result of giving both sides a big incentive to fix squawks and extend on-wing life), with total benefit that is directly related to numbers of aircraft built. The speed at which the alternative engine would pay off is related to production rate.
As the final struggle over the F136 neared, it became increasingly clear that the rosy promises of 200+ jets a year by 2016, and a 5000-jet production run, were not anything on which one could hang one's hat. The payback was getting later and smaller but the upfront investment was the same.
Interesting question - what about a CTOL/CV-only engine with a core based on the new 737/A320 engine? Would it be big enough and if so, would it weigh and cost less than the F135 with its oversized LP turbine and shaft?