I also wanted to post a quick update about that WBC as EDS idea. Ross Tierney (the guy behind the DIRECT concept) ran some simulations for me. Apparently for the specific design of the EDS, the 6-engine WBC wouldn’t quite work. Apparently the thrust on the RL-10s is too low to deal with the fact that the EDS has to put itself into orbit in the first place (since the Ares V doesn’t have the oompf to do the job all by itself) before it could be used for lunar transfers.
You might be able to get the design to work by going to RL10-Cs or RL60s if either became available, but your system would no be the same as the commercial WBCs, and wouldn’t have much of a propellant fraction advantage over the current EDS design. And you’d still be fielding new engines, and designing a whole new stage.
OTOH, if on-orbit propellant delivery became a reality, the standard WBC design would be substantially better than the EDS.
So basically, if you insist on having your lunar transfer stage pull double duty as a third stage to compensate for the fact that your booster can’t actually get its payload into orbit with two stages (because one of the two is a crappy performance SRB that is only being kept around because nobody wants a bunch of unemployed rocket nerds roaming the streets of northern Utah), then the Wide Body Centaur isn’t an option, and you better develop the Stick and that J-2X. If you actually want a real cislunar transportation system, you need to be able to transfer propellants on orbit, and at that point, the WBC is an excellent system to start with.