I can take this. It should be possible to push this touch-menu up in the z-order.. or arrange the window tree in a way that we don't have to.

It's also possible that this horizontal menu is just missing the right "menu" flag to already do that.

https://chromium-review.googlesource.com/#/c/chromium/src/+/1100668 fixes this.. 

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/7b8bbfb4014270ab8d6918434f784848ae34790d

commit 7b8bbfb4014270ab8d6918434f784848ae34790d
Author: Trent Apted <tapted@chromium.org>
Date: Mon Jun 18 06:26:28 2018

Ash: Ensure touch selection menus do not appear below the omnibox popup.

The touch menu is a regular popup bubble; using BubbleDialogDelegateView
to get the desired look with minimal effort. However, that engages its
CreateBubbleWidget(), which invokes widget->StackAbove(context). That
causes the bubble to stack _immediately_ above |context|; below any
already-existing bubbles.

That doesn't make sense for a menu-like Widget, so put it back on top.

This only really affects ChromeOS. Windows also uses this touch menu,
but the call to Widget::Show() already causes the Widget to stack on
top again.

Bug:  848327 
Change-Id: Icf115c69b0d0ca0e4a5af4ac6ce0f2b0c54c1678
Reviewed-on: https://chromium-review.googlesource.com/1100668
Reviewed-by: Scott Violet <sky@chromium.org>
Commit-Queue: Trent Apted <tapted@chromium.org>
Cr-Commit-Position: refs/heads/master@{#567938}
[modify] https://crrev.com/7b8bbfb4014270ab8d6918434f784848ae34790d/ui/views/touchui/touch_selection_menu_runner_views.cc