Developing magic that let him fly unaided shouldn't be difficult. Voldemort and Snape had both managed it in the original story, so there was even less chance that Avada, with his Magic Sense, couldn't do the same. Besides, he already had quite a few ideas about how to do it; he just hadn't tested whether they were viable yet.
And it came with another benefit: he wouldn't have to go to the trouble of developing a spell that made him completely invisible. If the Shrinking Horizon Charm could make his entire body vanish into thin air, what was the point of simple optical invisibility?
Even if he wanted to interact with objects in the real world while invisible, the Shrinking Horizon Charm didn't make a sound like Apparition. Combined with a well-practiced Disillusionment Charm, it would be more than enough.
"Come to think of it, Harry's Invisibility Cloak should be arriving soon, right? I can analyze it then and see what these so-called Deathly Hallows are all about..."
For now, he still couldn't move around in the space between spaces, so he couldn't let loose and have fun. After testing a few spells and confirming he could cast normally in the space between spaces, he returned to reality and continued toward the Room of Requirement on the Seventh Floor. He'd only gone to an empty classroom to test the effects of breaking the Apparition restrictions; his real research still had to be done in his private room in the Room of Requirement.
His current research, however, was fairly focused. Aside from the most important task of breaking through Voldemort's mental defenses, he only had to study Spatial Magic and try to understand the contents of Professor Baker's massive book.
But Voldemort wasn't on hand, and he'd just made a landmark