Convert .obj,.stl to .step

Yes, it is possible. There are a number of applications that can do this... eventually, I'll write a white paper on this subject, but for now, here a few apps that can help:
- FreeCAD
- Fusion 360 / Netfabb
- Geomagic Design X
- Various online converters
- InStep Studio 3D (my company's software)

I have not seen good results from the online converters. They are fine for trivial stuff, but nothing more than a few thousand facets. The same goes for FreeCAD which is ok for geometric shapes into the low thousands of facets.

The attached file contains different resolutions of the output, generated by our InStep Studio 3D application. The 11k size is probably about as big as you want to import into CAD, but it is also the most accurate. The other resolutions are still close too (try with the 1k3 size first to see if that is good enough). Note that if you want to do this yourself to get different level of detail, more points per NURBS or similar, you can do so using the free 10-day trial of our (or other's) software.

Let me know if this is helpful. Also, would you mind if I posted this file for others to see (won't do that unless you give the OK)?