Well, actually not being a programmer, I'm not fully aware of the limitations of GTK+...
But I feel deciding to keep the scroll bar puts limitations on what we can do.
Ideally, if you allow me to digress into a dream world, then ideally what I'd like to see is:

1. No scroll bar. Use swipes for scrolling. Can have a thin scroll indicator on right side, to give orientation as to where we are in document, but no scroll bar.
2. In full-screen there are two buttons only:
- full-screen toggle on lower right
- select-mode toggle on lower left
3. If screen is not touched for two seconds, these two buttons disappear as well, leaving virgin full screen. Touching screen makes the two buttons come back.
4. Tapping full-screen button causes the top and bottom bars to appear.
5. Now, the two buttons form part of the lower bar.

That would be an ideal solution for me...
Further, I think the 'long press for menu' is a good idea. But I think having to navigate a menu to come out of full-screen makes it slightly cumbersome...(the Image Viewer in Easy Debian has it) - I would much rather have a toggle button when I need it.

But again I am writing only as an end user who is blissfully unaware of the coding side of it :-)

So you guys are in a better position to weigh it all up...