The later 845s are in fact Gordinis, regarding valve and port size, camshaft timing, compression ratio, carburettor/distributor (on some of them fitted with Solex 32 EISA/Zenith 32 IF7).
The combination of larger carb/accelerator pump/vacuum advance makes a notable difference, mostly in mid-range torque.
There were two more powerful Ventoux engines fitted to R5s (36HP) and R6s (38HP). Both had standard valve sizes but hotter camshafts (R5: 20/56/53/23 , 7/7,1 mm valve lifts, R6: 16/52/52/22 , 6,99/7,43 mm valve lifts)
Dave, I don't think it's fair to compare the S800 engine with the Ventoux, judging only from their sizes...The Honda engine is a motorcycle engine put into a car almost by mistake. It's a free-revving engine, with double overhead camshafts, crossflow head, four carbs...it's reasonable to produce double the power (and, of course, to have less than half of the life than our engines).
Having done some fair amount of work to Mini engines, I always liked to compare them to Ventoux ones. I think that the A-series is a worse design than the Ventoux, in many places. But, there is a tremendous availability of "performance" accessories and parts (from camshafts to crankshafts to pistons to cross-flow heads to manifolds...) and that matters.
Sure enough, we could go the usual ways and install a hotter camshaft (no big deal to have an old one reprofiled), port the head, install a twin choke carburettor on a custom made manifold (Weber 36DCN for example, from a scrapped Alfasud), a less restricted exhaust etc.
But we are starting with a small bore / long stroke base engine (no room for larger valves, not suitable for high rpm). Although the connecting rods are light and strong,the crankshaft with its hollow big end journals seems weak (we have no option here!). And having these tall wet liners supported only at their base is also no good for high stresses. So one really has to spend a lot of money (and work hard) for higher engine output with reasonable durability.
However, nothing is impossible. The Dauphine R1093 engine (with domed pistons to give 9,2:1 compression, 9/50/45/7 camshaft with 7,06/6,97 valve lifts and twin choke 32mm carburettor) has an output of 55HP. There are 60mm (904cc) piston/liner kits available in France (pricey!) that give another 5HP, without touching the camshaft or valves! I guess that we can go even higher by installing the aformentioned R5 or R6 camshafts.
There was a French tuner back in the 60s who experienced with a "reverse" camshaft (to make inlet ports exhaust and vice versa), so he could install two twin choke carbs. Another one built a wonderful twin cam hemi head, both engines were said to produce around 80 HP. Not bad, I think...