As usual, Randall is dead right. Nevertheless, even as a non-Triumph chap I'm going to poke my nose in here.
If you're getting backfiring, by which I take it you don't really mean backfiring but small explosions in the exhaust on the overrun, that's caused by unburnt mixture, maybe with a little bit of additional air if you have s slightly leaky exhaust system. That points to a rich mixture rather than a lean or weak mixture, but is also a characteristic of CD carbs anyway..
I like the piston-lift method too, being careful not to lift too far which messes up the whole plot. However, I believe you have reached the ideal when, on lifting the piston, the revs momentarily increase then settle down again. If the revs increase and stay up, your initial setting is too rich, if the revs drop and the engine is "hunting", you're too weak. A tiny bit too rich is ideal.
With the idle OK, stumbling on initial acceleration can be due to too weak a spring, dashpot oil too light, or wrong needle. With your symptoms, I'd richen the mixture a couple of flats and try it again. If that doesn't work, put the mixture back and try a heavier weight oil. Then try both!
There are no universal truths, unfortunately. When the cars were new, no unworn components in fuel system or ignition, the factory could make settings confident that they'd be pretty much right. Which leads me to another question - how's your ignition timing and advance? I always keep in the back of my mind the old garage-man's saying that 90% of carburetter problems are ignition. Maybe a couple more degrees of advance might help?