That second list seems good in a lot of ways - interesting take on The New Batman Adventures and Superman - but I don't like its treatment of Batman Beyond. It should definitely come before JLU, if not Justice League. Among other things, even more so than "The Once and Future Thing", "Epilogue" simply doesn't work unless you've seen Bruce and Terry doing their thing for a while, and it's one episode that really deserves its full potential.
I'll agree with you wholeheartedly. I'll go one step further by saying
I made the list, and it
did have BB before JL.

It was placed firmly between STAS' "Legacy" and JL's "Secret Origins."
My opinions vary from the majority on some things, though. Some have theorized that ROTJ takes place before "Out of the Past." But I found that A.) nothing strongly supports it, IMO, and B.) it loses a lot of its dramatic effect if not viewed as the finale.
I mixed it up a little too, just for fun, by watching "The Call" after "Unmasked." It makes a better thematic finale, but it should still be viewed before ROTJ.
I also find it more enjoyable to alternate between BB and JL, in much the same way I did STAS and TNBA. It kept the events of Batman/Superman more vivid while watching JL, and it puts some of JL's foreshadowing ahead of the BB payoffs. However, this is just my weird way of watching it, so don't let me confuse you.
Lastly, I've said this before, but I leave "Epilogue" in its place between "Divided We Fall" and "I am Legion." Plenty of people have piled on the disagreements, but it just works better for me in every way.
EDIT: I'd also like to note that the TNBA/ STAS alternations were thought out, and not just random. Every cross-reference is safely explained. Example: Roxy Rocket's origin comes in "Utimate Thrill,"
before her appearance in "Knight Time." It just so happened that it worked to alternate after every other ep.