What is a practical way of burning the Challah portion that is removed from dough? Wrapping it in foil and leaving it in the oven would produce too much smoke for my house.
Aside from the foil or the above mentioned grill you can also sear it on a stove top burner. Alternately since it is so small simply place it in the oven while cooking the loaves. It need not be reduced to a cinder, simply rendered inedible. If you are getting smoke you have typically already passed the point of it being "burnt" and now you are starting to carbonize it.
My wife usually just saves them throughout the year, and then I burn them with the chametz.
Find someone with an outdoor grill, and put it under the metal, with the coals (or natural-gas briquette thingies).
If you live in a place with enough sun, consider putting a small 'solar cooker' on a window sill (or porch, if you have one). Consider whether the (albeit brief) smoking will draw concern and attention.
Solar cookers can even be built make-shift, if you need.
If you can't handle the smoke, get it out of your kitchen! That is, tell your local Kohein that you hold like Maharam of Rothenburg who, as quoted in Sefer HaParnas (written by one of his students) 111, was particular to burn the separated Challah portion in the house of a Kohein only. So now, dealing with the excess smoke is his
problem burden familial responsibility.