From the screenshots it does indeed look like all UIButtons where parented to the first one, so you can move them all as one. All except that first button were then hidden, as described above.
When creating so many buttons, another plugin that may be helpful is Keybindings (by AcidBubbles). It allows you to have a hotkey for duplicating atoms (in Desktop mode). So you setup one single button with correct colors, size, fonzsize, etc and duplicate form there, only changing text and trigger.