First, nice mandalas to @zoramite. Good concept, nicely executed.
Gluing can be very easy and fast if you use registration dowels. Just cut small precise dowel holes in the same spot on all but the top layer. (I use bamboo skewers, oak dowels, even rectangular pegs I cut from sheet material. Brass rods also work well.)
Then all you need to carefully align is the top, as it has no dowels for aesthetic reasons (or if you don’t mind the look of the dowels, just cut the top layer too). If the dowels are nice and tight you don’t need to wait between gluing the layer—it should all hold together nicely.
Here are three projects that use dowels to great effect to keep things aligned.