I believe the single cone transmissions should be avoided. I have never shifted a double or triple cone but it has to be a significant improvement.
The large single cone evolved from the T85 3-spd into the 4-speeds. Then they added over 50% more gear inertia by adding 5th and 6th and making the gears heavier (T56 weighs about 125#, right?). The single cone simply isn't up for the job.
I've heard running Mobile 1 20w with carbon fiber singles works good in the Ford Top Loaders which due to bigger gears and single cone make them hard shifting.
I don't think there is a full triple in the B-W or Tremecs - only a combination of triple and double. I solved part of my Gen 2 shifting issues by making a shifter extension turning it into more like a crowbar. Short throw shifters on singles makes them harder to shift since now you're giving away all the mechanical advantage you need to bull the sliders.