I've balanced the throttle bodies on my Thruxton, whilst not a speed twin the process will be virtually identical.
It can be done without removing the airbox as the manual tells you but it is fiddly process getting access to, and removing the blanking screw just to get to the adjuster.
there is a post here with some pics that may help
(4) Thruxton 1200/R Throttle Body Balance | Page 3 | Triumph Rat Motorcycle Forums
You may not have to remove as many things as shown, I didn't remove the breather just pushed it to one side, it all depends what tools you have, how small your hands are and how much patience you've got.
All the intake cover and bracket screws are pretty small and have the factory strong threadlock so a couple had to be eased out 1/8 turn at a time, I removed all the threadlock from mine to make it easier next time and replaced the security Torx blanking screw with a normal Allen screw as it gives more options for tools/bits to undo it.
Once you get access to the adjuster screw its a piece of cake, with the engine at normal temperature monitor the vacuum on Tuneecu (or whatever you're using) and turn the screw until its balanced. That post I've linked says its an Allen key but its actually a T20 Torx, you'll need a T30 security Torx for the blanking screw.

 

I’ve done my Speed Twin using TuneECU. It’s only reads out to the nearest 10hpa but a constant readout without fluctuation gets you almost bang in the middle. You can also hear the change as it goesin/out of balance. There’s a real crispness when it’s spot on.

Remove right hand side panel to enable more light into the work area. Unscrew the crankcase breather T30 Torx screw about 10 mm which is enough to allow the breather/oil trap out of the way. No need to remove the throttle body cover.
Remove the Allen bolt with a 5mm key to access the adjusting screw. Rotate accordingly with a T20 Torx key. Quick and easy job on the Speed Twin, I can check/adjust the throttle bodies in under ten minutes once the engines up to temperature.

DO NOT INSERT THE ADJUSTING TOOL UNTIL THE ENGINE IS RUNNING.
When the ignition is turned on the throttle butterflies open and close. If the tool is inside the body when it does this, something very very expensive in all likelihood will end up broken and the bike will not be rideable.
Do not twist the throttle (grip) when the tool is in place and the engine is running for exactly the same reason.

 

I've had airhead and oilhead BMW's, this sounds about as easy. Just need to take my time.
Thanks for the help guys!!

 

This is what I use on the adjusting screw, overall it measures 55mm, but crucially 30mm is what’s required to reach inside to turn the screw. The electrical wire connector block affixed to the shaft provides ample finger and thumb leverage to make precise adjustments.

 

Where did you get it?

 

It’s home made. The T20 bit was originally part of a much longer Torx screwdriver shaft.

 

Think a t-handle torx could be cut down and then grind two sides flat and use your fingers to adjust?

 

You'd probably only be able to turn the adjusting screw in one direction with so little rotational leverage. The shaft on that tool looks well under 10mm long, it definitely wont reach deep enough inside.
Whatever you use can't be too long either as you wont be able to insert into the hole due to the lack of clearance between the airbox and the throttle bodies.

 

Think this might work? Not sure how much room is in there. This is about 2.4 inches long.

Hazet 8802KV Insulated 3/8" Torx Bit Socket - Short, T20

Torx Socket - Short Design - 1000V - T20 - best deals on German tools and high quality engineering. Free same day shipping available.

www.kctool.com

 

I would say the Torx bit is too short and the handle is too fat.
I just used a normal T20 right angled key for the adjustment, although I think it was out of my security set because they were shorter than my standard set, even though its standard T20 for the adjustment.
Depending on how many parts you remove access can be tricky if you only have long reach Allen keys and Torx keys for example so having something you can sacrifice as @Kinjane did may help.
In the end I think I used a combination of my security bit set, parts of my 1/4" socket set and Allen and short Torx keys but that doesn't necessarily mean you need to buy all those things, going off @Kinjane description it sounds much easier on the Speed twin.

 

I'm using pod air filters on my T120, which makes access a breeze.

These are for reference to show the area exposed. I think used a 3mm hex to turn the adjustment screw.

There is a blank screw that is removed to gain access.