Difference and cartesian_segments yield wrong result

When computing the difference between two polygons that touch at one point but do not overlap boost::geometry::difference yields the wrong result.
In my original problem the touching point happens to be the starting point of the input polygon.

The polygons are unfortunatly very large and I only posted the code on WandBox
https://wandbox.org/permlink/0vqkFS71m0zJ65X4
Also, the problem seems very elusive, because when I tried to create a minimal example around the (presumed) problematic area, the bg::difference suddenly works. (has to do with the start point?)

The polygons look like this:
Green = inputPolygon
Red = subtractPolygon
Note that the start point of the inner green ring is the touching point.

The often suggested solution
*#define BOOST_GEOMETRY_NO_ROBUSTNESS*
seems to help in some cases:
https://svn.boost.org/trac10/ticket/13553
https://github.com/boostorg/geometry/issues/548
In my original problem defining BOOST_GEOMETRY_NO_ROBUSTNESS does help.
However, as also reported by others
https://svn.boost.org/trac10/ticket/13566
https://github.com/boostorg/geometry/issues/630
other (many more!) cases now fail.

**cartesian_segments**
In #653 I read about setting a higher precision (?) using "cartesian_segments".
This works much better than defining BOOST_GEOMETRY_NO_ROBUSTNESS.
However, in some cases it also fails.

I would like to better understand what this does
- Does the type "long long" define the integer type/precision used when rescaling?
- Assuming it would always work, which is not the case (cf. case 4 below), would it have any disadvantages?
- I noticed that the size of the DLL/so grew about 20%, which is OK, will the execution be slower?

**Here is what I tried (c.f. points 1-4 in WandBox-Code)**

1. The original problem with "default_strategy()"
This is wrong, the interior ring of the input (first) polygon simply disappears (instead of remaining intact)

2. The original problem with "cartesian_segments"
This works

** Minimal example **
I cut out a piece of the inputPolygon around the subtractPolygon to reduce the input.
Note that the green start point now lies in on the top.

Now the roles have changed...

3. The minimal example with "default_strategy()"
This is right

4. The minimal example with "cartesian_segments"
This is now wrong, a non-related corner of the input is chipped away (Blue=result)

The problem always seems to occur around the start point, could this be the problem?

I have reproduced the problem using
Windows 10, VS2015, Boost 1.66 on my PC
Linux, Gcc 8.1, Boost 1.66-1.72 on WandBox

Many thanks in advance!

**EDIT**
Shifting the start point (std::rotate)
- solves the problem in 1.
- does not solve the problem in 4.