The upper one looks like your best bet, but it is not made to fit a splined shaft like your transmission has. It would be way more work than it is worth to get it to fit.
I read it's description on the site you linked and it fits over a smooth shaft and is held in place with a single pin.
None of the other sprockets I saw at that site look suitable to me.
My question is: although this chaindrive set up is crude & brutishly Israeli, is there anything markably better or worthwhile available that would deliver better performance or be notably lighter, pending the availability of Staton's axledrive system?
I like the looks of your set up better than Staton's axle mount. Your engine sits higher and looks like it would be better protected than the axle mount he has. His 5:1 gearbox maybe superior than the Pocket Bike tranny that you are using, but If you are considering ponying up and getting the axle mount. I would first look into if you could run a set of freewheeling cranks. This would make your drive ratio variable, rather than fixed.
You/or your buddy's seem pretty ingenuitive in making that mount, you might be able to mount that engine on the top tube of your frame and run a chain down to a set of freewheeling cranks and utilize that cassette you have on the back.
It would cost less than a Staton Axle Mount, and you would have greater range/use out of your bike. It would allow you to throw it into low gear to climb hills, then you could throw it in high gear to cruise the flats.
I have a similar setup. It took alot of work, but, I love mine.
Check out: Scooterguy Tanaka Mount in Frame mount setups, to get an idea of what I'm speaking about if you don't understand what I'm saying. He is using the same 5:1 gearbox you are using.
Loosing the extra chain on the back wheel, will make your drive train more efficient, and utilizing your back cassette will make it more effective.
Again, you need to be able to get an adapter which fits. The adapter mounts on the splined shaft (14mm x 11mm x 6) on the gearbox, and the freewheel threads on to the adapter. As I mentioned earlier, you could use an adapter designed to fit a larger shaft, IF you use the appropriate shims.
I found 1 company in the U.S. which sells spline couplings which fit the splined shaft on the gearbox, but, they wanted over $30 per 2 inch coupling on single-unit sales.
I believe your best bet may be to take the existing sprocket, get it turned down to 3/4 or 7/8 inch, and have a key-way cut into it - essentially, turning it into a very short shaft for mounting the adapter.
The threads on the standard freewheels are 1-3/8 inch, 24 TPI (threads per inch.) (Offhand, I don't know the thread specs on the metric version.)
The size of the existing sprocket on the gearbox and the size of the freewheel sprocket appear to be similar; you just need to make sure that the total reduction ratios are correct (the new sprocket will be on a 1/2 inch pitch. The old sprocket/chain are often metric, #25 (0.25 inch pitch,) or #35 (0.38 inch pitch) chain on pocket bikes & scooters.
As far as Staton's freewheels; the White Industries freewheels are the best you can buy. They're expensive, but, they really are top of the line, manufactured to tight tolerances, and have a very strong racheting mechanism. The others are a lot less money, (but, are also not as reliable,) so, when setting up the system, you might want to use them initially, until you're sure that the sprocket ratios are correct. THEN, order a White Industries unit.
One final note. When using a freewheel on the DRIVE end of the chain drive that spins a sprocket on the left side of the wheel (when facing forward,) you use standard freewheels. But, when the freewheel is on the DRIVEN end (with a chain on the left side when facing the front of the bike) use a left-hand threaded freewheel.
However, if the chain is on the right side of the bike, reverse this, and use left-hand freewheels on the drive sprocket, and standard, right-hand threads on the rear.
If you don't follow this approach, your motor will be trying to unscrew the freewheel from the adapter (or hub.)
They're thread-on freewheel sprockets. An example of a shimano freewheel sprocket is shown below. They're designed to thread on 1-3/8 inch, 24 TPI hub. Staton makes several freewheel adapters, to allow you to mount a freewheel to a shaft. His adapters can be used on shaft sizes ranging from 1/2 inch through 1 inch. Available sprocket sizes for this thread-size range from 16 teeth, up through 22 teeth, and I believe I remember seeing a few 25 tooth ones. There are also similar, thread-on freewheels with a flange, so you can bolt larger sprockets up tp them.