I fully agree. Lee did have a third option also and that would have been to do as you suggest, bide his time in Gettysburg, while he allowed his troops some rest, strengthened his lines of supply and sent small foraging parties out to wreak what havoc they could in say a 20-30 mile radius of Gettysburg.
Well, yes and no. I can't claim any originality to the idea that Lee would have holed up around Gettysburg -- I got the idea from Shaara's book on Gettyburg, where Gen. Bufordis depicted as considering the possibility as part of his decision to stand where he did. He saw that if the Confederates were able to establish themselves in the area, the Union faced an expensive campaign of attacking uphill against entrenched forces to evict them -- the same problem that resulted in such bloodshed at Fredricksburg (and Pickett's charge, and elsewhere).
But beyond that, we need to look at the undoubted supply issues faced by the Confederates -- shoes, horses, and so on were in chronically short supply, for example. It clearly obviated the possibility of a long campaign against determined resistance; after all, the only reason they got as far as Gettysburg in the first place was because they had no opposition -- the Union wasn't even sure where they were.
On the other hand, I think the Confederate army would have been vulnerable to a seige had they remained in the Gettysburg area. They'd have had to fight their way out, eventually, or starve.
Lee had no line of supply. His army was living off the land, just as Sherman's would do a year later. Remaining in one place would defeat his goal of gathering food and supplies to take south with him when he returned to help tide him through the winter. By remaining in place then in a short period of time he wouldn't be able to feed his army.
That would have been suicide.
The longer he stayed, the more time the Union forces had to regroup and surround him, cutting off his supply lines and preventing him from defending Richmond. The Army Of Northern Virginia were all the effective forces the Confederacy had in the Eastern theater. Lee's job was to fight the Federal army, protect Richmond and threaten Washington DC simultaneously. He could not afford to sit on his ass 100 miles from his closest lines of supply and 200 miles from Richmond.
After the Battle Of Gettysburg - had he been victorious on July 3 - he would have had 45,000-50,000 effectives.
Due to the excellent railroad links near Gettysburg, the Union would have been able to eventually surround him with 150,000-250,000 men depending on how long he decided to sit around.
Had the Union brought up a couple of hundred mortars to target Cemetery Ridge, Lee's command would have been cut to pieces after they inevitably ran out of ammunition and then food.
Lee needed to smash the Union army hard enough to keep it from invading Virginia again for the rest of the season, he needed to stock up on whatever his troops could get their hands on - including horses, mules and beef on the hoof - and then get the heck out of Dodge.