Widgets are not guaranteed to work if they are extracted from the widget that is managing them. Developers of all the reusable high-level widgets assume that the internal widgets are only accessed and displayed through the public API that the widgets provides, otherwise they would never know what they can change in their implementation.
I would recommend to add whatever widgets you need to your own module. Code duplication should be minimal, because you only need to add a markup place widget and a push-button. If you find that you need to add more than a couple of lines of code then you can suggest changes to refactor the Draw Tube effect that avoids any need for substantial code duplication.
On a quick try, it seems to work more or less when reparented:
If the segment editor is next shown and the ‘Draw tube’ effect is activated with the mouse, then the scene of the re-parented point placement widget needs to be set again. But yours is private and hidden.
All this may just worth a try, may be it’s too much of an ugly hack as @lassoan advised.
A problem arise from otherwise straightforward solution:
cannot access all internal widgets of the above markupsPlaceWidget to disconnect the default established signals and proxy (i.e. connect) them to the effect’s markupsPlaceWidget slots (i.e. both default and draw-tube-logic ones)