The British East India Company (charted on Dec. 31, 1600, you hit that part exactly right) was the first of the proto-corporations that were organized to expedite the great trading and exploration voyages.
(Parenthetical note, this was only made possible, or it might be better to say useful or desirable, by the defeat of the Spanish Armada in 1588—prior to that the Spanish and the Portugese had a deathgrip on the spice trade.)
Prior to this new type of organization, with the creation of a fictitious persona, the corporation, any investor would have been personally liable for any losses of the venture, to the entire extent of his personal assets.
The release from personal liability afforded made it much more easy to organize and finance these extremely risky operations.
Now, with that out of the way, I will take a bit of an issue with your placement of the date of transition from nationalism to corporatism, for the following reasons:
First, if one would like to argue this date marked the first appearance of limited liability fictive entities, that would be incorrect. The early Middle Ages saw the first of these, in the form of towns, universities and religious orders. Later, the principle included guilds. This was established in English common law by the 14th century.
The other way to argue this would be to mention that this saw the first application of the concept to private enterprise and for profit entities, that is technically correct. However, charters for these enterprises were for purposes only seen by the granting government as in it's national(istic) interests. They were private tools of public policy.
It was not until after the onery American colonists revolted after 1776 was there support for enterprises unrelated to the direct public interest. (Alexander Hamilton was an early champion of the idea) Still by 1800, well over 95% of all the corporations chartered in the States were for purposes of thngs like building and operating bridges, roads, canals, and other public service tasks.
Finally, in 1811, New York enacted legislation that enabled corporations to be charted with nothing much more than a statement of the intended purposes of the business. Many of the other states took until the 1850's to do so. England did in 1825, and the other European countries followed soon after.
So, based on this, I would argue that the first part of the 19th century is the earliest time that can be considered the birth of an independent corporation. If I were forced to pick the point at which the transition to a corporate state began, I would argue that it happened immediately after the Civil War. The urgencies of the war required consolidation of the railroads, setting the stage for the first real national super-corporations with the wealth and power to influence politicians, and therefore public policy, an exact reversal of the status of the British East India Company.
If we go along those thoughts then, perhaps the start of the corporate state can be traced back to May 10th, 1886 with Santa Clara County v. Southern Pacific Railroad Company where corporations could be considered a “fictional person” under the Fourteenth Amendment of the Constitution:
Section 1. All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the state wherein they reside. No state shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any state deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.