The Beis Yosef and Darkei Moshe cite numerous reasons to justify the common custom of not tying Tzitzis on an outer garment despite having 4 corners. Some of those rationalizations are relevant our jackets as well. Therefore, there is ample support for not looking unusual and wearing Tzitzis on your jacket.
Generally, short jacket never is split the majority, but this could be an issue with a frock/kapota, although they are custom made for frum Jews and always shave a rounded corner. The issue is most relevant for coats.
If the front bottom corners are rounded as common on a single-breasted jacket, there is no requirement for Tzitzis at all. If they are basically square like a double-breasted one, they would count as square, as even a Tallis does not have perfectly sharp corners like Tefillin do.
So, if your double-breasted coat has a large slit and square corners and you feel that you want to be Machmir and not rely upon any of the Beis Yosef and Darkei Moshe's justifications; the appropriate place to tie the Tzitzis would be the 4 bottom corners and not the lapels. However, I don't suggest doing this. As my Rosh Yeshiva once said, "There is an Inyan to be normal".
As a side point, I have seen some long jackets in Yerusholaim where the lapels are rounded, presumable to avoid any question of having four square corners.