We have a History PhD in our midst, it seems
! I need to start reading about the Eight Route Army, I never heard of them...
Here are my two historical cents
. The Empire is very much like the Soviet Army in 1941, badly depleted, badly led (the Dark Council is very reminicent of the Military Council of Soviet Russia pre-1940; Inexperienced, politically powerful men with a penchent of culling their own ranks, rather than that of the enemy) with a significant manpower problem. However, unlike Soviet Russia, the Empire doesn't have the numerical superiority which allowed the Soviets to swallow defeats like Kharkhov or Kiev while learning to adapt to their own deficiencies.
The Empire can compensate by, firstly, taking a page from Stalin's playbook. After 1941, the command structure of the Army was significantly flattened, allowing, ironically, for the Soviet juggernaut to act with unheard of operational flexibility. I.e. curb the power of the Sith in the army or assign special tacticians that could advise the Sith generals without fear of reprisal.
Second, reform. The Empire needs to institute a reform of its military along the lines of Gaius Marius in 107 BC and loosen its racially discriminating guidelines for conscription. Marius drafted his legions from the poor citizens. the Empire has slaves and aliens. They can either do it now, or use it as a desparate last resort, like the Spartans or the Confederate South did (Spoilers: didn't go over so well).
Third, strategic reimagining. The problem with the Empire is less about its manpower problems, and more with its antiquated way of imagining war and, as a result, can be fixed by learning and adapting to their new reality. The only two campaigns that were even remotely succesful by today's standards were Hoth, where the idea was to tie up crucial Republic elements with misinformation and deception, and Ilum, where ground way gained, then progressivly given to secure a tangible resourse, while suffering relativly light casulaties. In contrast, the Core Worlds Campaign was very much Germany circa WW1. Balmora was for the Empire what Russia was for Germany in 1918 - a stretch of land you needed a million men to secure, while keeping those men from being mobile and effective elsewhere. Corellia was like Germany's Michael offensive, an impressive and succesful land grab with no clear long-term strategic objective except to hold as much ground as possible (Spoilers: didn't go over so well either
If the Empire adopts these three changes, then it will have a chance to continue fighting the war on equal footing. Win? Probably not, but fight? Definately.