Just been through some of the same issues on mine Morris (late iron head, inch and an eighth) and some of the same to-ing and fro-ing between carburettor and ignition and back and forth.
It started with a rare and uncharacteristic extravagance - I bought a new 389 to replace the 1 1/16th 376 I'd been making do with (and running very happily on) for years. Bad Plan when something ain't broke . . .
Well, would it run right? Exact same spec as yours, down to the last detail, and no it wouldn't - but the machine ran fine when I put the 376 back on (and off, and on, and off etc). Coughed and spluttered and generally was a pig to ride with the new carb. No good at no-load low revs (all spit and cough and flames), no good at mid range (hesitation, flat spots and spitting occasionally), only ran right on main jet sorts of openings, and was a dog to start hot. So I turned the slide down to reduce the cutaway, played with the needle height (and with pilot jets same as you - no difference) and eventually got it to run a lot better but with much too rich a slide. Far from spot-on though.
Thought it was at least OK for a decent blast, so took it for 100 miles last week. The last 30 miles were awkward 'limp home' miles as it got worse than ever and it was chucking it down with rain, of course, as it always is if you think you're about to grind to a halt.
Now the deterioration was odd, as carbs don't just have hissy fits like that. So having spluttered home - just - I did a quick and overdue check on the mag, and found a messy dose of constant winter muck and damp had made a mess of the contact breaker and, more serious, that the fixed point mounting block wasn't properly attached - the securing screw had backed off a bit. So I was getting irregular points gaps, varying between correct and near-zero. Good, I thought, that's that fixed then, maybe it's been the cause of other woe too, let's give it another go. But no, with the 389 it still wasn't as good as it should be. (But it was beautifully-mannered, again, with the old 376 shoved back on.)
So, following the advice of one of our savviest folk here - thanks a lot Brian! - I junked the brand new needle jet this afternoon, and put in one I've had for at least 35 years.
Total and utter transformation, and normal service resumed at a single stroke (well, with a bit of consequential fiddling with the pilot air and slow-running).
It's often said that some of the offerings in the new carb department are awful, but general consensus I thought was that the Amal/Burlen jobs do what they say on the tin. Not my experience with a new 928 concentric I was given for another project last year (which I ended up swapping for a 389 in the end to achieve another transformation), but I thought maybe I was just unlucky. Now I think I'll be recycling original carbs, of which I've got a small shelf-full, rather than try any more of this new stuff.
Cheers, Bill