Would an 8% reduction in drag outweigh the weight addition from this custom CFD-tested winglet?
First off, awesome question and great investigation! This kind of let's-see-what-happens inquiry will take you far should you decide to pursue aerodynamics at an advanced level (and, of course, in other pursuits). Not so long ago, I had to write a similar report: lacking the resources and knowledge of the aerospace giants, I, too, wondered why I could seemingly invent designs that on the face of things appeared vastly superior to theirs. I thought that I had winglets down cold.

Then I went to work for Boeing and started talking to the aerodynamicists. I started graduate study of aeronautics. Turns out, unsurprisingly, that there's a lot you can't get out of undergraduate textbooks and publicly available data. While I obviously can't be exhaustive here—and probably won't even answer your question to the letter—I can give you a few things to think about. To be clear, I wouldn't go much further than you have with your modeling and simulation, but if you'd like some discussion points for your paper here are some in no particular order. I've made some assumptions about your level of knowledge, so please forgive me if it's patronizing and ask me if you need clarification.

The fidelity of your baseline model


  The winglets...were those of the 737MAX....The wing is the same as that of a 737NG.


On what data did you base your model? The wing of a 737 is not a simple matter of an airfoil, some taper, and some twist. I notice that you did not include nacelles/pylons or flap-track fairings. The design of a production winglet is heavily tied to the integration of the overall wing design, including all of the extra components hanging off of it.

The reason that the 737 MAX winglets are effective

The 737 MAX uses what's branded as the Advanced Technology (AT) winglet. We know that a well designed wing extension is more aerodynamically efficient than a winglet. But the 737's wingspan must stay within certain limits in order to operate with the same ground infrastructure as previous models, so a winglet is a good solution. But what if we could have a little of both? Well, the AT winglet does exactly that:


  The lower winglet is configured such that upward deflection of the wing under an approximate 1-g flight loading causes the lower winglet to move upwardly and outwardly from the static position to an in-flight position resulting in an effective span increase of the wing.


So to really understand the efficiency of the AT winglet, you'd need to model this deflected geometry.


The other contributing item to the effectiveness of the AT winglet is its natural laminar flow:


  On previous winglets, the drag due to friction from the airflow over the winglet is one of the main detractors from efficient airflow....this is solved by Boeing using detailed design, surface materials and coatings that enable laminar – or smoother – airflow over the winglet.


The flow regime you're modeling

The AT winglets are most effective as their efficiency is aggregated over long, high-speed, high-altitude cruise legs. All you've given is a true airspeed, but for this kind of analysis of transport aircraft the Mach number is much more important. You haven't provided an air temperature, but from the density you've given it looks like this simulation is at sea level, which means your Mach number is not high enough. But this in fact might partially explain your results. Observe the drag curve:

In general, a spiroid winglet like yours reduces the induced drag at the expense of some parasitic drag. As you can see, we can afford some extra parasitic drag at lower speeds because the induced drag dominates.

If I were to make one suggestion, it would be to run your simulation at a realistic Mach number (around 0.8) and see what happens. But beware...

The limitations of your CFD software

We are getting to the point where CFD, when implemented well, is quite good for modeling aircraft performance in cruise flight. Much of the wind-tunnel testing for large aircraft these days is focused on high-lift and maneuvering conditions, where CFD falls much shorter. Of course, we always want to validate our CFD in the wind tunnel for all flight conditions, but for well-understood configurations in cruise the results often match well in terms of calculating overall performance. But the "when implemented well" caveat is key. I personally don't have experience with SOLIDWORKS Flow Simulation, but it looks like it's designed to be a general-purpose CFD software, so I would not trust its results too much for large, complex, high-speed simulations such as the ones required for this analysis.

In particular, there is the issue of turbulence. Not in the sense of unstable air that jostles an airplane around, but in the sense of chaotic flow over the aircraft's surface. So chaotic, in fact, that no computer in the world can accurately model the motion with a sufficiently short computation time. Instead, we use turbulence models that try to approximate what's happening in a way that can be solved quickly enough. SOLIDWORKS uses the k-epsilon model, which is popular for general-purpose software but might not be the best choice here. In particular, notes Wilcox,


  Even the [k-epsilon] model's demonstrable inadequacy for flows with adverse pressure gradient has done little to discourage its widespread use.


As flows over airfoils are quite influenced by adverse pressure gradients, I would exercise caution. I can tell you that Boeing makes good use of the Spalart–Allmaras turbulence model in conjunction with detached eddy simulation (Spalart is an employee). But choosing the correct CFD implementation for a particular problem is a nuanced process requiring a great deal of judgement and care.