With hindsight, it's clear that the optimal strategy would be focusing on naval superiority (capturing major rivers and ports) and fomenting/supplying Unionist revolts within the South in regions that were strategically important/easily defensible (West Virginia obviously, but also East Tennessee, South Texas, etc.). If they can free the local slaves sooner, even better for your cause. Critically, leave Virginia proper alone until the very end of the war (i.e. until you could attack simultaneously from the north and south), with just enough Union troops in the area to break a potential siege of D.C. if necessary. It's the most defensible area of the Southeast with all those smallish rivers and mountains and the martial culture gave the Confederates their best officers.
The Union had an overwhelming advantage in men and materiel so it didn't really make sense to abandon a theatre. The Confederacy would gain much more by sending Lee and most of the Army of Northern Virginia west than the Union would be attempting a strangulation tactic. And even if we handwave that it would have been absolutely politically impossible for Lincoln to tell the public he was refraining from sending Union armies into Virginia.
Not saying avoid VA entirely. I'm thinking more like build a strong line of fortifications from Leesburg to Centreville to Dumfries or so after First Manassass and dare Lee to attack it. There would be equal pressure from Confederate leadership to keep significant resources defending Richmond no matter what. Either do the late VA encirclement I described or bait Lee to pyrrhicly attack D.C. and get your Gettysburg a year or two early.