About this one, never since I came to Japan have I heard this expression. Dai-nippon-teikoku several times though, which for me seems better suited than Dai-to-a.
I also like kibo better for the tech goal, as well as Heian-kyo for the culture one (bushido is not specifically related to culture), but these are more personal preferences.
I chose Dai-to-a over Dai Nippon Teikoku because of an important distinction.
Dai Nippon Teikoku refers to the actual nation-state itself and does not properly illustrate the intent of the goal in and of itself.
Imperial Japan, for most of its years, only consisted of Japan proper, Corea, Taiwan, various islands and Manchuria.
Which doesn't fit the description of the goal very well.
Dai-to-a on the other hand, is an expression of the concept of the Greater East Asia Co-Prosperity Sphere, which is codified in the description of the goal. So while the state is an impermanent thing, this concept helps us to understand the context and intent, and remains useful in perpetuity.
In short, it's whether you want the name of a nation-state, or the name of the driving concept for the goal, which I would lean towards the latter.
A similar comparison would be if we chose between "British Empire" and "The Sun Never Sets".
Also similar would be "50 States of America" as opposed to "Manifest Destiny".
About Kibo, I think Flying Geese Paradigm better tackles the intent of the goal.
As it was a term coined by Japanese scholars themselves, and explicitly references Japan's role as the most advanced East Asian nation.
Kibo only represents an impressive feature of Japanese technology but isn't in and of itself representative of the drive of Japanese ingenuity in anyway by itself.