Sense 2a has been influenced in meaning by fortunate. It has been in standard if not elevated use for some 70 years, but is still disdained by some critics. Sense 2b, a blend of 1 and 2a, is virtually unnoticed by the critics. Sense 1 is the only sense commonly used in negative constructions.
You could not have arrived at a more fortuitous time.
… the intensification of competition on the job market has only exacerbated our class anxiety, as hiring seems all the more uncertain if not fortuitous. —Jeffrey J. Williams, College English, November 2003
… he is a brilliant candidate not despite his anti-intellectualism but because of it. He has stumbled upon a fortuitous moment in which the political culture, tired of wonks and pointy-heads and ideologues, yearns instead for a candidate unburdened by, or even hostile to, ideas. —Jonathan Chait, New Republic, 20 Dec. 1999
Her $170, 000 bid on what is now Matanzas Creek's vineyard was accepted. The south-facing slope was a fortuitous find … its worth more than 10 times as much today. —Jeff Morgan, Wine Spectator, 15 May 1996