I like it. Will definitely consider it. 

I'm a little concerned about visual clutter and problems with visually differentiating between the open tabs and the recenty closed tabs (what part of the tree am I looking at now?). Particularly because I want to draw the recently closed pages tree with the same awake-vs-hibernated rows style that is applied to the regular pages tree (allowing hibernated tabs to be removed and un-removed).

Currently I am thinking I will start with the separate-pane approach, then later add an option to show it at the end of the pages tree as well.

I like the idea. I do want to avoid "options overload" though, so I may need to think about rearranging or subcategorizing the options a bit more before I add this. That being said I suspect many people would like to tweak this.

OK I understand.

The ability to switch themes is planned, this will also allow you to create your own themes and graphics.

Adding an option to hide the row-hover buttons is also planned.

Pretty sure I got this fixed for the next release. It seems if I first set focus to the Chrome window that will have the New Tab tab in it, then create the New Tab tab within that window, then the omnibar keeps the input focus. So far, this fix has worked properly 100% of the time here.

1. I will consider adding this. The main thing I need to think through is how fine-grained of control the options should give over which buttons should have which behavior (on hover, always show, or never show). So far I have had requests for "never show any" and your request, "always show close".

2. This should be fixed in the next release.

I'm planning on the following:

1. Add 'Duplicate tab' context menu item 
2. Add a dedicated 'Recently closed' sidebar pane which can be used to do the 'Reopen closed tab' function
3. The following other new context menu items are under consideration: Close children, Close tabs below, Close tabs above, Close other tabs, and Hibernate/wake equivalents of these; and 'New tab' and 'Reopen closed tab' items. If these are added they will most likely appear after context-menu-user-customization is implemented, and most or all of these will be hidden by default.
4. Add a dedicated 'Bookmarks' sidebar pane and an 'Add to bookmarks' context menu item which will (hopefully) allow adding whole subtrees of the Sidewise pages tree as a bookmark or bookmark-folder(s), including remembering hibernated tabs.

Are there any other functions that you currently access via the tab bar which would not be covered by this?

I'm planning on the following:

1. Add 'Duplicate tab' context menu item 
2. Add a dedicated 'Recently closed' sidebar pane which can be used to do the 'Reopen closed tab' function
3. The following other new context menu items are under consideration: Close children, Close tabs below, Close tabs above, Close other tabs, and Hibernate/wake equivalents of these; and 'New tab' and 'Reopen closed tab' items. If these are added they will most likely appear after context-menu-user-customization is implemented, and most of these will be hidden by default.
4. Add a dedicated 'Bookmarks' sidebar pane and an 'Add to bookmarks' context menu item which will (hopefully) allow adding whole subtrees of the Sidewise pages tree as a bookmark or bookmark-folder(s), including remembering hibernated tabs.

Are there any other functions that you currently access via the tab bar which would not be covered by this?

I'm planning on the following:

1. Add 'Duplicate tab' context menu item 
2. Add a dedicated 'Recently closed' sidebar pane which can be used to do the 'Reopen closed tab' function
3. The following other new context menu items are under consideration: Close children, Close tabs below, Close tabs above, Close other tabs, and Hibernate/wake equivalents; and 'New tab' and 'Reopen closed tab' items. If these are added they will most likely appear after context-menu-user-customization is implemented, and most of these will be hidden by default.
4. Add a dedicated 'Bookmarks' sidebar pane and an 'Add to bookmarks' context menu item which will (hopefully) allow adding whole subtrees of the Sidewise pages tree as a bookmark or bookmark-folder(s), including remembering hibernated tabs.

Native Chrome GUI: Chrome currently does not provide a sidebar API for extensions, so until they do this is probably not possible. Please star this Chrome request if this is something you'd like to see.

Toggle hover icons: planned.

Toggle hiding solitary window node: under consideration. The ability to add top level "Groups" -- basically special "folders" that sit at the top level alongside Window nodes -- is also planned, and I need to think through how that would work if the solitary "real" window's node is being hidden.

Chrome doesn't provide any mechanism I know of to do that - neither from an extension's code, nor manually by the Chrome user.

Might be worth requesting this on http://crbug.com