Will try some experiment, i am near sure your will don't do this, or maybe even do this the way i will regret i ask, but think this might be an interesting experiment anyway.
So, first of all, what your ask is impossible to implement. Some time ago i investigate this problem actually and there is really only bad solutions to it. There is no way how tree can be maintained if you run an extensions like "New Tabs At End". The best solution is not to use it. Many time was spent to work seamlessly with original Chrome ordering which your seems hate, the other orderings is a next major step, and a big one, not sure this will be soon, will not give false promises to you, and by the way i like the Chrome default.
The saved tabs your see is from the last session most likely (from you last total Chrome close), this is actually a bug, as they must be deleted actually, but meantime this extension is not work very well in scenario when "reopen on restart all my tabs" is enabled in Chrome.
And it is not recommended to use this mode actually - much better is close-save all the needed tabs using the Close-Save all Open windows button in Tabs Outliner, and then, on next restart reopen only the really needed tabs. Also in chrome you always can reopen a window you close using the restore last closed window (from context menu in Chrome Sidebar, or from menu in the bottom of the any new tab)
Despite all of this, and the fact the when i see your G+ profile, and read that you have 130IQ and see a bunch of "no track" extensions and the fact that you "HATE", and a completely normal way to manage the tabs is a "bad bad bad" for your, the first idea i have is that most likely there is simple stupid to ask anything such a person ; ) I will try anyway, simple as experiment.
So the request:
How about to go in reviews and to help this project by setting 5 star ; ) Yes i am not satisfy your, but at list spent my time on this issue - will be cool to see some reciprocity.
Most likely you will use this extension and i think you interested in its success, this will really help attract some more users, and along with them there will be more chances to bugfixes and new features. And who know, maybe i will even implement the Opera ordering if many users will ask this (the best way is to post this as feature request in
tabsoutliner.userecho.com and leave it to collect votes of other users, i will definitely do this if there will be many up votes for such ф feature).
I will be very grateful for such a act.
And many other users who will find this extension because of this, also (yet only in some karmic way ; ).
Also worth mention that setting anything below 5 stars will do actually a harm, so if you cannot set 5, better not set anything at all. Of course if only this is not your aim - "to show something". Will be also slightly grateful if you dont do anything instead of setting 4 o r 3 or 2 or 1 star, as many former firefox/opera haters do already... but the 5 stars will really amaze me ; )
Also i decide to do something for my own live in result how will you vote ; ) So please do this - very interesting : )
Best regards, Vladyslav.