I don't own or have access to a Triumph so can only speculate based upon a bit of experience with the Omega and drawings from the manual.
Below pic shows the mechanism
and an enlargement of the areas of concern
Take this post for all its worth - it is speculation and should be used only at your own risk. Modifying the trigger mechanism will surely void your warranty.
The two areas indicated by the green arrows are the sear points between the hammer piece and trigger piece. Take note of the circled areas in the lower drawing. The centers of each green circle are the points of concern. The parts (if like the Omega's) are cast and finished in such a way that a light ridge is left all along the center of each piece.
VERY lightly honing those two surfaces in such a way so as not to change any angles nor remove any depth beyond that center ridge might give you the trigger you want. Be extremely careful to not change any angle or go too deep into those surfaces. You just want a smooth surface at each contact point.
And that's about all you can do. The top picture has blue arrow which is pointing to one angled leg of the trigger's torsion spring. Very carefully reducing that angle (straightening) that leg might reduce pull weight slightly, but without a Triumph in my hands, I can't say for sure.
Whatever you do, do it slowly and meticulously and realize replacing those parts might be expensive. Creating a dangerous trigger would be far worse.