You kind of have to game the export system to get the extended specialization. I had to build a Trade HQ with an Electronics extension, build a trade port with 3 processor depots, and then turn off processor exports until I had 23,000 crates of processors stored (which very nearly killed me. Had to take out multiple bonds, turn off education and public transit systems and raise taxes to a ludicrous degree to keep from going bankrupt), and then turn exports back on to get the 1.5 million in a day required to build the Consumer Electronics HQ. You probably have to do something similar for an Oil extension.
Oh, and the very foundation, my oil field, has less than a month remaining and was unable to fulfil the requirments for extended petrolium HQ improvements,