Let's assume that the inset gap length used by the questioner means the width of the inset gap, which is the dimension along the same direction as the patch width. One antenna textbook says that the inset gap length commonly is 3 times of the feed-line width. However, if the feed-line width calculated by rotmanlens is used here, then the inset gap length will become 8.58 mm(=3*2.86), which is even larger than the patch width! Therefore, you may forget this rule of thumb (i.e. 3 times of the feed-line width) and take your actual problem into consideration. Anyway, the inset gap length influences the resonant frequency and input impedance by introducing parasitic capacitance.
PS: I have modified the statements for clarity.
To romanlens: I agree with u qualitatively on your comments on the feed-line width. I have no intention to evaluate your calculation results.