Two EDS, no waiting
Remember that back in Apollo, there were several engine burns that had to take place after the CSM + LM stack was in earth orbit. The S-IVB fired again for Trans-Lunar Injection. The SM engine fired once for Lunar Orbit Insertion. The LM descent engine fired to de-orbit the LM and land. The LM ascent engine fired once to get the astronauts back into lunar orbit. The SM engine fired a second time, for Trans Earth Injection.
Some things are different in NASA's "Apollo on Steriods." The EDS is used much like the S-IVB, but the LSAM descent engine steals the LOI burn from the SM. Otherwise, the analogues are still performing the same burns that they did in Apollo.
My thought is that it will be more cost-effective to employ two EDS in a lunar architecture, while using a smaller LSAM descent stage. My logic is that the EDS will already be in production, and its tankage will be simple and cheap to fabricate. The LSAM descent stage will be more expensive, consisting of multiple propellant tanks which are designed to operate in 1/6 G.
My "two EDS" architecture doesn't employ any techniques that NASA would deem risky, like waiting until lunar orbit to perform the first rendezvous between Orion and LSAM. Orion will dock with LSAM as currently planned; the only difference is that Orion will have an EDS attached to its aft end in order to perform the LOI burn.
When looking at the "DIRECT launcher" proposal, I'm struck that, despite using two rockets of similar or equal lift capacity, the two payloads for most of the architectures are very different in mass. One rocket will launch the Orion CSM, while the other launches the EDS and the LSAM. In my mind, it makes more sense to off-load the mass of the LOI propellant from the LSAM, and then give the Orion CSM a second, partly-fueled EDS that will be used for the LOI burn.
In the current architecture for DIRECT-II (use of stock RS-68's instead of improved versions that only exist on paper,) the 3x RS-68 first stage and the baseline EDS can put 101.9 tonnes into the chosen assembly orbit. Assuming that one launch of DIRECT is used solely for the ~25 tonne Orion CSM, that's only 126.9 metric tonnes in the assembly orbit. This is probably less payload than the ill-conceived "1.5 launch" strategy using "Scotty Rocket" and "Zubrin Rocket" (Ares I & Ares V.)
NASA will probably fault DIRECT-II because it won't be possible for a single DIRECT/Jupiter rocket to launch their baseline LSAM and EDS masses in one throw. I propose that NASA should baseline a lighter LSAM and take off the LOI-burn requirement. That way, the two payloads in the DIRECT-II architecture will be a lot closer in terms of mass, and the architecture can make best use of the 203.8 tonne capability that two DIRECT/Jupiter boosters could place in an assembly orbit.
I realize that the architecture I propose has some drawbacks. The EDS tankage will undoubtedly be heavier than the LSAM tankage it will be replacing, although the specific impulse of the engines will be similar. Also, because the EDS launched with Orion will carry a small fraction of its total propellant load due to the needs of the LOI burn, it will be a pretty inefficient use of the EDS mass. It also introduces an additional two engines (2x J-2X on the EDS) into the lunar architecture, which causes the loss-of-mission probability to go up slightly. Finally, the higher inert mass of the partly-fueled LOI EDS will increase the amount of propellant that the TLI EDS must burn.
My solution to the inefficiency of the EDS is to design a "stumpy" EDS that will be correctly sized for the LOI burn. Alternatives would be the use of off-the-shelf Centaur or Delta IV upper stages in place of the "stumpy" EDS. Studies will have to demonstrate that a replacement stage would be capable of performing the mission in a cost-effective way.
In short, DIRECT Launcher is probably the best way to run a government-driven lunar exploration program in these times of constrined budgets. At the same time, NASA is looking for any way to invalidate DIRECT, and they will likely exploit inefficiencies in the architectures for DIRECT missions to the moon. I propose an architecture that makes better use of the tremendous capability that DIRECT can give us. The two-EDS architecture forces NASA to revise its LSAM baseline, which is something the agency is loathe to do. Then again, it's best to change the LSAM at this stage in the game before any proposals have been submitted, rather than wait until later when Congress has killed off the Ares V as "too expensive" and the moon has already been lost.