Ha! I've grown Yellow Twist Bud and Harrow Velvet (Burleys) and Bolivian Criollo, and I looove the taste, but - some leaves are just overwhelming in a pipe. I believe it's a combination of alkalinity and the initial harshness of freshly air-cured leaf, with absolute nicotine content playing a minor role.
For example, I can smoke a long Toscano cigar (= strong Kentucky, aged for 12-24 months) without getting affected, but a small piece of that in a pipe may give me hickup.
(1) Aging is supposed to help. 3-6 months minimum for Burley, better a year. My Bolivian Criollo is now >1 year in storage, it's difficult to say how much smoother it has become, or how much lower the nicotine content already is - some leaves are just much stronger than others.
(2) Washing. The "Toscano" book I've mentioned here before describes that leaves are soaked upon arrival at the factory's premises in tepid water for about half an hour. They used to sell nicotine-extract based pesticides as a side product.
I've tried that - it indeed lowers the nicotine impact and makes the leaf "milder", but also a bit more bland. If it undergoes a strong fermentation afterwards like the Toscano, that probably won't matter, since the tobacco's aroma gets altered a lot, but for the pipe I feel like I'm missing something here compared to the untreated leaf.
(3) Casing with sweetening substances, i.e. sugar or licorice. That's generally done with commercial Burley (and almost all commercial pipe tobaccos for that matter) to the tune of 5-20% of tobacco weight. I've tried all sorts: Maple syrup, licorice extract, anise oil, brown cane sugar, glucose, invert sugar, honey, grape juice, rum, Ouzo, sweet liquors like Cointreau. I like the results of this experimentation to a varying degree. It does solve the nicotine absorption problem by increasing the pH of the smoke. It also made me aware that store bought pipe tobacco lives to a large degree off the aroma of burning sugar. In the end of the day, I always prefer the unaltered leaf.
(4) Toasting: Seems to help somewhat, esp. when cased with a sweetener before. It alters the taste slightly or dramatically, dependent on temperature, length and moisture.
(5) One "natural way" of adjusting the alkalinity is blending / mixing with some sweeter (high sugar) leaf. For example 50% Burley + 50% Virginia ("Half & Half"), or 40% Burley + 40% Virginia + 20% Orientals.
Now I like the Burley aroma as it is (esp. the "room note" pure, unaltered Yellow Twist Bud produces). After a lot of mixing I have come to the conclusion that the addition of just 20% of a sweet Oriental (e.g. sun-cured Prilep or Samsoun) are enough to make the Burley mellow and avoid the "nic hit", while mostly maintaining the original Burley scent. 20% of flue-cured Virginia do the trick, too.
(6) If you have a pipe which can take 9mm active charcoal filters, try that. It removes a good amount of nicotine and very alkaline tobaccos become less aggressive (i.e. what people call "alkaline bite" quite disappears). I found strong Burley to be actually more tasty in a charcoal-filtered pipe.
(7) Leaf ripeness at harvest. In previous seasons I've grown mostly Orientals and Havanas, and learned that I much prefer a certain "cigarishness" over an "overripe" taste, so consequently tried to harvest at "maturity" rather than "ripe".
Now, with the Burley, which naturally produces few sugar, I see that leaves picked when mostly yellow air-cured to brighter colors (almost yellow or a light orange). These leaves burn with much less alkalinity, actually with a touch of sweetness, are very mellow and don't give a "nic hit".
Leaves harvested green (with just yellow tips) air-cured nicely to a beautiful red / tan colour. They have a fantastic aroma, too, but swing the big hammer. I do hope aging does good things to them, but will in future prime Burley at a riper state.
