Wayne, with a trident, there is no necessity to even leave a branch. When you chop the trunk to a bare stump, you will have new buds pop all over the remaining trunk. If you air layer (I had good success in the past with cutting a groove and driving in a large wire or a deep carving will work too), it should sprout below the layer in the same way.
If you chop it, I'd still try to root the piece you chopped off, as it is a shame to give it up so easily.
Also: If you chop it, leave some extra length and chop it straight across. The tree will provide plenty of buds to choose from, but somehow if you chop at an angle, it will bud at the low end of the cut and not at the top, necessitating another chop later on.
Good luck and I look forward to seeing what you do with this one.
Chris