I am trying to work with what you have done. Let us assume that the shorting of F and D on the dynamo led to a high voltage from the dynamo (which it would) but this high voltage would only wreck electronic components. Unless sustained for several minutes, I would not expect damage to the coil, or to the condenser(s). You say that you have two, and that they are physically larger than the usual type. There is potential for failure here, but it does seem unlikely unless the condensers are totally unsuited to the job. But changing them for a standard condenser is neither expensive nor difficult.
Going back to what happened today, my first thought is that I always start an Ariel with the throttle slightly open. Yours ran for 30 seconds, sounded lumpy and stopped when you touched the throttle. In 30 seconds of running of a bi-starter Square, I would expect to have gone to bi-starter completely off. I can't remember ever needing to use even half bi-starter to move off on the bike, unless it was start, into gear, move off then shut the bi-starter, all in rather less than 30 seconds and then in very cold conditions. The Solex carb is a cunning device and I expect that opening the throttle richens the mixture as a first step above tickover. So if the bike was running lumpily, opening the throttle without shutting the bi-starter might simply have over richened the mixture to the point where the engine stopped. Attempts to re-start with the bi-starter in full choke position would give an over rich mixture and so it wouldn't go.
Can I suggest going back to the set up where the bike started today and seeing if it will start again. If it does, quickly go to half bi-starter and open the throttle a bit at the same time, or open the throttle slightly before you go to half bi-starter. Assuming it continues to run, keep the throttle open whilst you shut the bi-starter completely.
If it won't start, try to clean the plugs using a wire brush. If they appear to be clean anyway, still give them a brush but pencil the points of the plug. To do this, take an HB pencil and apply the end of it as if you were drawing a line around the plug points, along one side, across the tip, then along the other side. Why this works I still cannot fathom, but I have known it start engines which were otherwise completely impossible to start. It is a trick I learned on Platelayer's trolleys powered by JAP V-twin engines but I have used it successfully on a 2-stroke scooter which stopped outside our house, much to the astonishment of its teenage owner.
Let us know how you get on with this. If you don't even get the bike to fire, it is time to look wider.
36 4G, 37 VH, 54 KH(A), 75 Healey 1000/4, 52/53 ex ISDT KHA (project).
Former Machine Registrar & Archivist, General Secretary and Single Spares Organiser (over a 25 year period).
Now Archivist once more - but not Machine Registrar.