Reverted r85922 and related: new doTableStuff(). I copied in the old doTableStuff...

Reverted r85922 and related: new doTableStuff(). I copied in the old doTableStuff() from before r85922 and reverted all parser test changes that looked vaguely related. Apologies to Platonides, since some of his parser tests appeared to be relevant to the old parser, but it's simplest to just revert all the related changes and then re-add any useful tests later. See CR r85922 for full rationale.