I don't have Surly chainring but Truvativ for which I could find no definitive answer on flippablity, but advice that it was probably possible. So I flipped mine just to see after it had exceeded 20,000km of which over 10k was in my ownership, and the rest was an estimate of the original owner who had owned the bike several years prior but was uncertain of actual distance traveled. My bike came 2nd hand also with its original rear sprocket which I flipped on acquisition when fitting a new chain to replace the Shimano chain from original purchase.
I will be replacing both chainring and rear sprocket sometime soon, but I'm pushing to see how far I can push the original items and maintain rideability. My rear socked is looking very worn already but despite my apprehension, I am amazed that I'm still riding trouble free in the drivechain department already 3000km over my initial goal of reaching 10,000km before replacing chain, chainring and rear sprocket with brand new items.
I'm passed the 13,000km mark last week and other than readjust my rear sliders (no eccentric on my non-Thorn Rohloff bike) for chainwear since shortening the chain at 10,000km, I am just amazed and astounded how this old worn combo keeps working reliably and without incident despite looking much more worn than yours. I do expect to eventually reach the point where I cannot flog my dead horses of spockets and chain any longer. But I am beginning to really enjoy how this worn out combination of components still turning and turning and turning.
From experience, on a derailleur bike I would have got through at least 3 or 4 chains, the same number of cassettes and at least 1 chain ring in 13,000km of my ownership of my bike. With original (reversed) chainring and original (reversed) sprocket with 23,000km (or more!) to their name, my bike is JUST on it's 2nd chain!
Note that my bike is mostly used for commuting and no long tours where I might end up stuck in the middle of nowhere. I would not recommend pushing components to the limit I am experimenting with if you are likely to get stranded assuming your bike components will withstand the same abuse.
A Rohloff equipped bicycle is truly a remarkable machine, not just in terms of the technical wizardry in the hub. But in the longevity and reliability of those external drivetrain components compared with derailleur bikes.