Bonneville Starting Problems

I have an '06 Bonneville with original carbs. From new it became more difficult to start if left unused for much over a week. This has steadily become worse and now, at 55000 miles, the fuel/air mixture is critical for the engine to start from cold.
In the first six months of use, on three occasions the engine stopped after running through heavy rain on dual carriageway roads for six or seven miles. The Triumph dealer's mechanic told me he had seen this on a few "high mileage" bikes, presumably owned by riders who dared to ride their bikes in all weathers. After playing a hose pipe on the front of the bike with the engine ticking over for ten minutes, when it never missed a beat, he gave up except to apply silicone grease to the LT terminals of the ignition coil.
I subsequently discovered that encasing the ignition control unit (under the seat) in a piece of old bicycle inner tube and sealing up the ends cured this problem of the engine stopping in heavy rain, presumably because it shielded the ignition unit from the spray being thrown up by the rear wheel.
However, two years ago at 38000 miles, travelling home from work in heavy rain, the engine started misfiring and next morning resolutely showed absolutely no sign of life. I removed the carburettors, washed out the small amount of deposit in the float chambers, removed the jets and blew them out and also cleaned the fuel tank filter. The engine would then start, but not easily, so I replaced the ignition coil with an HT-1 variety from ElectrexWorld, which fixed the problem for the next 18 months of regular use.
Last December, I went to start the bike one morning, but although it would 'hunt' and try to go, it wouldn't actually start. Eventually, I have now replaced the ignition pick-up coil (setting the air gap to 1.0 mm: 0.8-1.2 mm recommended, but originally set to 0.4 mm) as well as the sparking plugs, and over a week of evenings checked that the bike will start without a problem, although it is now critical to pull the choke out by the correct amount (in fact, I pull it right out, then push it in slightly). This last Monday morning, I went to start the bike to set off for work on it, but again it would hunt but not start. I had forgotten to switch off the fuel tap the previous evening, but at other times that has simply meant using a bit less or no choke when starting.
There is plenty of fuel, I can smell it. The fact that the fuel is six months old will not seriously affect starting, since when I previously fixed the starting by clearing the carbs and fitting a new ignition coil, the bike started fine on fuel which was nine months old.
The only other thing which I can see is that the spark does not appear very strong. Trying a brand new, spare HT-1 coil makes no difference to the intensity of the spark.
So within the last 17000 miles, I've cleaned the carburettors and fuel tank filter (the latter more than once), replaced the ignition HT coil and pick-up coil and there are new spark plugs fitted.
My questions are:
1. If the problem lies with a weak spark, is this down to the ignition controller output? Could it be that having received a sufficient wetting in the past for it to stop working (although leaving the water to drain away from it for about half an hour always allowed the engine to be restarted) has affected it; and this has resulted in enough corrosion or degradation of the control unit for its performance to be reduced to the point where the spark is so weak that the petrol/air mixture required for starting has now become critical?
2. Is there any other part which could need replacement, which I have so far missed (ignition or carburettor)?
3. Is there any other ignition system which is known to work well with the Bonneville? In principle, any electronic ignition system can be used, providing there is a trigger pulse supplied to it and the ignition HT coils used with it have the correct primary resistance to match its electronic characteristics.

 

Thanks for the link, Half Ton. I rang up and spoke to the guy at TT Power. The Firestarter unit has good reviews, so I've ordered one (before 3 pm, for delivery tomorrow). I'll let you know how I get on with it.
TTP also have air filters and jet kits for tuning, which look interesting. Jenks Bolts website also sell kits and a useful tuning guide at http://www.bonneville.se/nedladdning/CJK6.pdf

To Recycled Rocker, no I haven't tested compression yet, that's a bit further down my things to do list. Electrickery is OK if you do one thing at a time then test the result. Coils on older stuff work fine when wet providing the low tension leads are sealed from the wet at the connector and the top of the coil is kept clean and free from oil residue.

 

Jenks Bolts tuning guide is at http://www.bonneville.se/nedladdning/Hur man jettar.pdf