This is great stuff. A couple of things came to my mind -
Without the major campaigns in the west, would the skill of Grant and Sherman and the others be discovered and utilized in the east?
Also, how would the situation change if the Confederates stuck to a purley defensive strategy, causing no Sharpsburg or Gettysburg?
I do not think that anyone would have paid much attention to Grant in a world were he eventually actually lost ground,with Bowling Green and some other Kentucky towns in Confederate hands,and lost 25000 troops when they surrendered,essentially(for a month or two) leaving the way open to invade Ohio(although the Confederates regard this as too extreme,and dont act on it,aside from advancing through and holding a good part of Kentucky before the Unionists manage to build a new Western army)I have Sherman being killed,too,not unlikely,being a sort of Union Stonewall Jackson as he was.If A.S Johnston lived,things would gone a lot better for the CSA.The Confederacy needed time to discover its not-terrible Western generals,and I can see Davis appointing the Texan overall Commander of Confederate forces west of the Appalachians.Nathan Bedford Forrest would have risen through the ranks to become one of the leading Western generals also,moving from just a cavalry colonel to general of Confederate forces in Kentucky and Tennesee.Joseph E.Jonhson,Kirby Smith also would have increased in importance.Awful ones like Pemberton(the guy who lost Vicksburg)and Braxton Bragg,John Baylor,John Bell Hood and Bearegard would have been moved away to something less important or dismissed altogether.
That probably would have been a great idea.Lee could have stayed on the defensive and allocated more troops to more widely defend Kentucky, and the ports like New Orleans,to prevent any sustained or substantial penetration into Confederate territory.The Confederacy had only to defend itself successfully for a limited period of time to convince the North to simply give up and go into negotiations.Lees invasions of the North were stupid ideas.They wasted ridiculously large numbers of supplies and troops that were badly needed to stop Grant.Well,by modern standards Confederate losses were quite light.But cpmpared to things like Vicksburg and the various fort defensive battles on the Atlantic coast,they were very large.What Lee should have done is defend northern Virginia and pay more attention to defending Kentucky and Tennesee.Then,defend the coasts more vigorously with more serious town garrisons and a bigger Confederate Navy.Further,the New Mexico campaign should have been executed more vigorously,if say Albuquerque and Tucson came under Confederate control,there would be nothing to stop a Confederate cavalry campaign through a comparatively very lightly defended West.That would have provided the same aweinspiring show of force the invasions of the North provided,without severe,setpiece battle defeats.Sometimes I wonder what the strategic objective of the Maryland and Pennsylvania campaigns were.Maryland had a considerable Confederate element(making up somewhere around 15-25 percent of the population)but it was never enough to bring the state over to the CSA.It was,in essence,a Northern state.Pennsylvania,of course,

..If taking Washington was the objective,than it still was a bad strategy.taking Washington was possible but very difficult.The Confederates would have sustained the same(maybe worse?)attritional weakining that they took in OTL.Through the Civil War,you can see that,except towards the end of the war,whenever the Confederates were on the defensive in the Eastern Theater,they were winning decisive victories.Things like Manassas,Charlotteville,and Fredericksburg,come to mind.And they werent pyrihhic victorys,with the Confederates slowly being beaten down.If he had continued on this strategy,he would have won eventually.