I agree with everything Dan said.

I sometimes wrap some tape around the inner cable before I cut it.  That reduces the chance that it frays.

I prefer the Sram cable cutters.  They work well on shift and brake cables, as well as outer housing.  I checked, SJS does not sell it with the SRAM logo, but it looks like this one with a different name on it.  Mine (Sram) has red handle, not yellow.  The awl in the handle is great for making sure the end of an outer  housing hole functions well after cutting it.
www.sjscycles.co.uk/tools/jagwire-pro-housing-cutter/

But SJS also have much cheaper cable cutters too.

I assume you are aware that Rohloff shifter cables use brake outer housing that is NOT compressionless outer housing.  No need to use the compressionless shifter housing that is sold for derailleur bikes.

I do not know why your frame would have two sets of cable stops on the downtube for a frame built for a Rohloff.  Perhaps the frame builder did not realize that Rohloff cables have to have some slack, that there is no reason to use bare cable along the downtube.  But for aesthetics, do it any way you want.

I have started using Dan's suggestion for superglue on the end of the cable to reduce fraying, that was a great idea.  But it has to harden before you use it, you do not want to accidently glue the cable tip to something.

If you use your bike for touring, it would be a good idea to make sure that both cables are exactly the same length, and cut a third cable to that length too in case you needed to replace a cable later on a tour.  If you already have a cable cut to correct length, it simplifies cable replacement.  That means that the outer housing length for both cables should be exactly the same too.

I see PH made some comments while I was writing mine, I agree with everything he said.

Not something I've come across. 
If it's doing it consistently, can it be replicated when pulling away?  I'm thinking you could change gear with the cable disconnected and see if that makes a difference.  Though it'd be hard to do that on the move!  You might also try it with the cables slacked right off.  With all hub gear issues, working out if the problem is within the hub or elsewhere is a huge advantage. If you can get it to do it while on a workstand or upside down, you might be able to hear or feel where it originates.
Good luck.

Thanks.  Might try that.  But wouldn't the glue make the cable a bit bigger, and, therefore harder to get in the housing?

I have a custom road bike equipped with a Rohloff.  Since my bike shop no longer works on them, I have to deal with the nightmare of replacing the cables.  (Take me about 4 - 6 hours total, as I end up ruining about a half dozen cables -- too long!  too short!  cable totally frayed after putting it in the housing cable! -- before FINALLY getting it (semi)correct.  Almost makes me want to go back to a traditional drivetrain.  My bike has the cable braze-ons at the top and bottom of the downtube.  Therefore, mine is set up like a traditional road bike with 2 sets of housing cables -- from the shifter to the top braze on, and from the bottom one to the gear box, with only the bare cables on the downtube.  I'm wondering if part of the reason I have so much trouble is because I'm doing that, rather than one long housing the entire way.  That won't look as clean, as I'd need to use zip ties to secure it, but could that make the installation (somewhat) easier?

Mike, this is a long shot, but have you tried striking the axle end with a soft-faced mallet or shoe sole?

I know Rohloff have suggested this in cases of excessive friction/quick spin-down, not for noises like yours. However, i do recall one post here indicating it was also helpful in addressing an associated "noise" but I don't recall specifics. If I can find it, I'll post the link

A quote from Rohloff's site I saved to my files offers details...

Check the smooth/light motion of the sprocket by rotating this backwards. If you notice excessive resistence, then the free-floating (sprocket side) bearing may rest under tension and will need to be loosened. Do this by thumping each axle stub with a plastic mallet sprocket side once, then gear mech side once). Sprocket must now rotate backwards smoothly with little resistance.

An unlikely solution but free and harmless, according to Rohloff. If the nature of the noise changes, it might help narrow the hunt for a cause.

When you do find a solution, please let us know the cause, as it might be helpful to others in the future.

Best, Dan