As you say, McClellan did not fully commit at Antietam: fully a third of his troops never saw the battlefield that day. So, although he numerically had a 2-1 advantage, in terms of troops on the field, it was more 4-3, with the "3" holding good defensive position. But, as you also note, some of the Confederate numbers arrived on the field just in time to keep Lee's flank from being overrun - earlier in the day, it wasn't 2-1, or 4-3, but something like 3-1, and 2-1. McClellan had overwhelming numbers, even holding some reserves, if he had moved quickly. "McClellan" and "moved quickly" were rarely in the same sentence. If he were playing in today's Poker World Series, he'd be the guy hemming and hawing over every bet, then cautiously betting as little as possible - never "all in".
Ursusminor has done some re-enacting, and some years back, she & I went to the Harper's Ferry Christmas re-enactment. While she did her "bit", I wandered the town and the event. Afterwards, we drove up to Antietam for the annual battlefield Luminaria - really, really cool. They put up a luminaria for each of the 20,000+ casualties of the battle, and intersperse camping re-enactors throughout the grounds. I highly recommend it, should you have the chance. But, get there early - the line starts forming a couple of hours in advance, and goes about 2 miles long.
Getting back to Gettysburg and the invasion of the north. It's been my impression that, in addition to the reasons already noted, there were two other rational for the move into Pennsylvania. First, the months spent fighting in Virginia had taken a toll on crops, infrastructure, livestock, etc. The Army of Virginia struggled to find basic supplies there, on which to live and fight. Pennsylvania looked like a fat breadbasket to them. Second, the Confederacy was seeking formal recognition of its' existence from Britain, France, etc.., and the economic advantages that might arise should the Union blockade now be formally interfering with European nations trading with an officially-acknowledged nation. In short, if the CSA was a real entity in Britain's eyes, and the two nations had a trading relationship, then the Union blockade would run the risk of angering Britain, and perhaps English frigates would be called upon to enforce Her Majesty's trading rights.
Carrying the conflict onto northern soil, instead of constantly being on the defensive, would make it easier for the Confederacy's representatives in London & elsewhere to make the case for formal recognition. "See? We're carrying the war to them! See what they're newspapers are saying, about settling this, about suing for peace! This is gonna end soon, the North is losing its' resolve. Lincoln won't win re-election, and the new administration will work out a settlement. And, you know how much you love our cotton, and you know how much we love your manufactured goods, so, let's make this official, shall we?"
It helps to remember that it had only been about 50 years since British troops burned Washington, DC., and less than 90 since the revolution, Yorktown, etc. - there wasn't the warm "first among allies" relationship that has existed between our two nations for nearly 100 years now. The United States was still an upstart, crude, PITA reminder of one of the Empire's most embarrassing losses - and, Lincoln, that rube born in a log cabin, self-educated lawyer from frontier Illinois, almost epitomized the caricature that England had of their "American Cousins". Remember, Jeff Foxworthy still gets laughs about redneck jokes - to Great Britain, the Empire on which the sun never sets, with centuries of history, with the bluest bloodlines - our whole country, especially Lincoln, was a redneck joke. They had little reason to love the United States, and some interest in dividing it, and taking it down a peg. If the south succeeded in seceding, well, that might be a good thing in London.