Hey Irish guy... Let me help you out a bit on understanding carb set up for the CVK's and what shimming needles does... My set up is somewhat similar... air box carve with Staintune exhaust. I also have the Pieman reprogram done to the ignitor, that while not being strictly "mandatory", it does optimize the ignition timing curve to take full advantage of the intake and exhaust mods... I will also add that my set up has been verified via dyno testing to give me the air fuel ratio that I was after, across the board... and should put you in the ballpark, tuning wise. Also, comparing the "torque feel" between a 360 engine (Bonnie) and a 270 engine (America) is really difficult. The 270 configuration is totally different in how and where in the rpm range, it delivers its torque.
The ABSOLUTE FIRST thing you need to KNOW, regardless of anything else... is what is in your carbs now... You can guess all you want... and that's what you'll be doing... guessing... If you don't know where you're at now, you can't make the proper adjustments. The flip side of that is to assemble a small "jetting kit" before you even tear into the carbs, have everything on hand and then just install your desired package.
Also, tuning carbs is all about the inter-relationship between the pilot jets, pilot screw position, needles (shape/profile & shimming/height) and the main jet size. They all contribute to the air/fuel flow at various throttle positions and there is effective overlap between them. If you google "tuning Keihin carbs" you will come across articles that will show and explain this.
Let's start with the Pilot jets... you can use either 40 or 42's... they will overlap in their effective range... But to get a 40 to "flow" enough you need to open the pilot screw around 3 to 3 1/2 turns to "equal" a 42 at 1 to 1/2 turns out... So you are at the end of the effective tuning range on the 40's at the point that they need to be typically set with a set up such as yours... I recommend 42 pilot jets with the pilot screws ~ 2 turns out for your set up.
Needles... ahhh... the black art of needles and shims... Ok, the needles meter the fuel coming out of the main jets and affect the amount of flow and at what throttle position that flow comes into play via needle diameter, profile (shape) and height. Keihin offers over 100 various needles for the CVK... don't worry... we're going to look at just three...
The stock 790 needle basically has the profile of a nail... and when used without any shims, brings the main jets into play very slowly. This, along with the cam profiles, creates a "torque dip" between 4 & 5k rpms... Shimming (raising) the needles helps bring the mains in sooner but the straight, "fat" profile is still not optimum for addressing that "dip"... Per the Triumph dealers service manual, Triumph uses two different profiles now, the "Thruxton needle" (used on Thruxtons & Scramblers) and the "865 needle" used on everything else... I have found that the "865" or NBZT coded needle along with one GENUINE Keihin shim works best on my set up. When looking at my torque curve from dyno runs, this has just about eliminated, or has minimized, the "torque dip" typically found in the 4 to 5k rpm range.
Main jets... this is really the easiest variable to deal with... all it has to do is flow enough gas at wide open throttle to match up with your air flow and give you your desired air/fuel ratio, typically around 13 to 13.5 to 1... Depending on mufflers used (effective flow) and your general elevation (air density), within set ups such as ours, main jet sizing between 140's and 150's is typical, give or take a few points either way. 145's are spot for me...
Ok... so now we have an idea of what gets us proper fueling across the complete throttle position range... Here's what I would recommend: assemble a jetting kit consisting of 42 pilot jets, a set NBZT needles and 4 GENUINE Keihin shims (they are flat ground and not punched out, as a washer is. And they give very finite, predictable and repetitive adjustment), and a range of main jets (I would think that 140, 145, 148's would cover your needs. add 142's and 150's if you want to have all bases covered). Look at your carbs and see if they still have the (soft) phillips head screws in them or have they been converted over to the stainless hex screws... If they have not, buy a set from one of the vendors (Mike @ BellaCorse has a kit)... cheap enough and then you won't strip out the heads and it makes doing "insitu" carb adjustments a lot easier. you should be able to assemble all this for around 50 bucks or so... I would go with the 42's, screws 1 1/2 to 2 turns out, NBZT needles w/1 shim and the 145's... install that set up, see how you like it... and then find a good dyno operator and take your bike and jetting kit over and see exactly where you are... and you should have what you need in your kit to make any needed adjustments...
If you want to get maximum "enjoyment" out of your 790 set up, I HIGHLY recommend that you contact Mike (Pieman) at Triumph Twin Power to have your ignitor reprogrammed... This will pull all your engine mods together and you'll be surprised just what a 790 engine can do... If you do the reprogram, you WILL need to install Barnett "green" clutch sprigs... as I can guarantee that you will get clutch slippage at upper rpms... the stock springs are not strong enough to hold the plates together... and no, there is not much increase in lever effort... With the above mods, you should be making around 70 rwhp and 50 lb. ft. of peak torque... with a base of around 44 lb. ft. and rising quickly...
I hope this helped and wasn't too long winded...