You seem to be assuming Lee had the larger army and you make no reference to Union casualties in all those battles and you are assuming in any case, the Union did not suffer heavier casualties ? If so I am assuming you are incorrect.
I'm not assuming Lee had the larger army (in the Seven Days). I'm looking at all the possible ways of getting the strength of Lee's army, and comparing them to the same strength metrics of the Union army.
Lee's army comes out larger. It has more men AP, more effectives (it has more effectives in those units after 20,000 casualties in the Seven Days than the Union force had in those units after 15,000 casualties in the Seven Days), more regiments (it has 215 regiments, the Union force had 175 regiments) and more officers.
In actual fact, the most important long-term result of Bragg's invasion of Ky. was the delaying of the North's inasion of the Confederate heartland for a year, which extended the war in the West by a year. In other words , the war in the West would have been effectively over with the surrender of Vicksburg, in 1863, allowing the Union to bring all available forces to bear on Va.
So the 1862 invasion (conducted without assets from the East) has a delaying effect.
But that is not what we are discussing here; we are discussing the alternative options for what to do with Longstreet's corps in 1863. Are you proposing an 1863 invasion could have the same delaying effect again?
Again, that does not deny the fact that the loss of Ky in 1862 , could have changed the war in the West, nor its ramification in the halls of various European Foreign Offices, than one more dreary battle in Pa. and Lee in the end back on the Rappahannock.
Even though Bragg's invasion failed, does not change the fact that it was a bold strategic move to retrieve Southern fortunes in the West. He tried and failed, but, in concept, planning and execution, even in failure it compares more favorably than anything Lee attempted, or even, I suggest, thought of.
But you're talking about the possible outcome of a
success for Bragg (in 1862) versus the outcome of Lee
not succeeding (in 1863).
If Lee had succeeded in 1863 in a battle in PA (not "one more dreary battle in PA" but the only major battle in PA in the entire war) to the extent that was plausible given the actual events - the same metric by which you are judging Bragg's "could have changed the war" - then that would be Lee defeating the Army of the Potomac and crippling it*, rendering it unable to effectively take the field against him and making him master of PA for weeks. Even if he doesn't then have the chance to follow up and destroy the Army of the Potomac, he has the ability to strip Pennsylvania of forage, compel massive Union redeployment
out of the West and to the East, wreck Union communications around Baltimore, and force Harpers Ferry to surrender.
Delay
This has massively delayed all Union offensive plans, including in the West. Troops are needed to rebuild the strategic situation around Washington.
Even once rebuilt the Army of the Potomac is missing most of the veterans, and if it's rebuilt with Western veterans then those veterans aren't in the West.
Domestic war opposition
This kind of thing happening in PA is going to be bad for the re-election chances of the PA governor. The Army of the Potomac is also going to need rebuilding, which means more recruitment; given the situation in late 1863 and into 1864 that means conscription, which was unpopular. It's also trivially true that suffering massive defeats is bad for the popularity of a government and a war.
Foreign intervention possibility
A significant defeat like that makes foreign intervention more likely. The spikes and declines in foreign intervention being discussed overseas were related directly to events in the East first and foremost.
And, of course, Lee can then send troops west and have Chickamauga happen "on schedule", or at least not have it
not happen.
* the requirement for this to happen is fairly minor, as Gettysburg was a very close battle; a properly done echelon attack on Day Two would do nicely.