Thought I would come back and update my situation, and say thanks to everyone who provided input to my Rohloff neophyte problem. Special shout out to Mickeg, who replied first and also pointed me towards the gearing modeller, which was invaluable, along with the Sheldon Brown calculator to confirm my workings out. As a measurement specialist, I value the opportunity to use at least two tools to measure something in order to check the reliability of my output.

Brief recap: I was trying to decide on gearing for my new Rohloff-equipped Smithy Mule. My goal was to match the bottom end of my current go-to bike, a 1997 Litespeed Obed. It has a low of 99.3 gear inches (3.1 mph at 60 rpm) and a high of 17.3 gear inches (29.5 mph at 100 rpm). I'm also switching from 175 mm cranks to 165 mm, to save my already-wrecked knees.

Update #1 (desired speeds and cadences):

On a 5-day C2C tour in the UK, I paid special attention to my speeds and cadences. Although I didn't climb any "long and steep" climbs, there were some "long and middling" climbs (such as Hartside Pass at 15.1 km, with 540 m of climbing and sections at 12%), and several shorter, steeper climbs (with some sections at 20%). I didn't need to stop or walk on any of these climbs or sections, although I did need to use my lowest gear frequently. This confirms that my new bike needs to go down to my Litespeed's lowest gearing, or even slightly lower.

Update #2 (what I learned from using the various modellers):

(a) After much work with the Gates Sanity Checker, it eventually dawned on me that this was oranges and apples - the numbers on a Gates chainring have no relation to teeth on a regular chainring! I had forgotten that I originally was thinking of a Gates belt, which is why Chris at Smithy had pointed me towards the Gates modeller. So I scrapped my Excel page of extensive data from the Gates modeller. Doh.

(b) From using Sheldon Brown's calculator and the gear-calulator.com site, I realised that comparisons (between the two, and to my Litespeed calculations) was confounded by the lack of standardisation between the two. For example, Sheldon has a 27.5 x 2" tyre combination and a 27.5 x 2.5" combination, but nothing in between. I intend to use a 42-44mm slick on the roads and a 2.3" knobbly off-road; neither modeller had these. Not a big deal, as you can do calculations either side and guesstimate what's in between.

Update #3 (where I have arrived at):

First grateful discovery is that the two modellers generally agreed, within rounding (Sheldon calculates to 1 d.p, gear-calculator to 2 d.p.). Phew.

I ran calculations for the following parameters: (a) 38mm and 50mm (Sheldon)/51mm (gear-calculator) tyres, as these were closest to my intended 42mm and 2.3" tyre plans; (b) 165 mm cranks; (c) low cadence of 60 rpm and high cadence of 100 rpm. My 5-day trip confirmed this is about what I use when going very slowly up a steep hill and very fast on a downhill, respectively; (d) 38T chainring, as the new frame will fit up to 42T and this gives wiggle-room for upward adjustments if needed, and is a fairly large-ish chainring.

Combining the results for the two tyre sizes, a 38x18 combination gave me 2.7mph (60 rpm) to 25.1 mph (100 rpm) and 15.3 to 84.4 gear inches. 8x17 combination gave me 2.9mph (60 rpm) to 26.6 mph (100 rpm) and 16.2 to 89.4 gear inches. 38x16 combination gave me 3.1mph (60 rpm) to 28.3 mph (100 rpm) and 17.2 to 95.0 gear inches.

I have focused on the bottom end to make a decision, as this is the more important end for me. I discarded the 38x16 combination, as it is either the same low end (38mm tyre) or higher lower end (50mm tyre) as my Litespeed.

I'm swithering as to whether to go with 38x17 or 38x18. I guesstimate that the 38x17 combo will give me the same low end as my Litespeed if I use similarly sized tyres (2.2"), and a lower low end if I use the smaller tyre size. The 38x18 combo will give me a lower low end than the Litsepeed for all tyre sizes I would use - but limits the top end to about 24 mph to 25 mph. On a level, smooth road with a following wind and day-trip luggage, I reckon I'd rarely hit 25 mph, and would certainly not sustain that speed for a long period. Going downhill, meh, if I have to coast, fair enough. On my 5-day trip, I saw very few people power down (i.e., pedal down) long hills, and my days of trying to see how fast I can get are gone. Over 6 recent days of cycling, all with downhills, on a relatively unloaded bike, my max daily speeds were 22.0 mph, 25.0 mph, 29.4 mph, 31.1 mph, 31.9 mph, 32.0 mph and 32.0 mph, respectively.

Sorry, lots of information! If anybody has an opinion on the choice between 38x17 or 38x18 above, I'd ppreciate it, but I think I can hardly go wrong with either.