I see no issues with the Clone to Stormtrooper transition - Prequels established Sifo-Dyas placed an order for the army without the Jedi's knowledge, giving Palpatine an army to combat the Separatists. The Clones were bred to follow orders and be the best soldiers, but the Jedi Generals turned the clones on to being more free thinking and individual. Palpatine planned for this with the Order 66 organic implant, which made both the Jedi's fall and the clones Order 66 trigger all the more tragic. Not only were many Jedi dying, but so too were the clones betraying their Jedi friends against their will. Post Order 66, clones began age out of service and Palpatine opened recruitment to all citizens of the Empire. This worked in his favor for a variety of reasons. The new show Rebels revealed that Imperial Academies used training as a way to discover force sensitives, sending hopeful recruits to the ISB to make a choice - join the Empire as dark side agents or die. Of course, being an oppressive regime, the Empire pretty much implies to its citizens that those who fight for them as Stormtroopers will be safer than those who don't. I'm sure Imperial officer's families don't get hassled as much or taxed as much.
Basically, I can easily see the Clonetrooper ranks being replaced with open recruitment of Stormtroopers in greater numbers. However, given the Empire is eager to recruit as many citizens as they can, this leads to less experienced troopers. This makes it easier for the Rebel Alliance to fight the Empire, as these aren't Clonetroopers they're dealing with. I don't see the Death Star as an answer to a dwindling army, as the DS and the DSII were under construction before the Stormtroopers even existed. The novel Tarkin notes that the battle station was being built before the Clone Wars even ended, which Tarkin found odd but he didn't much care to investigate further.