Interesting thought, but the situation is more complicated so it might not work that simple.
About EU, there's one very important factor - US provision of security umbrella to all its members including Germany after WWII - and this makes integration easier for all members despite all their differences. Russia is isolated out of the picture, Pax America.
Now take a look at the Asia Pacific, and imagine there is no PRC, then it would be another EU right? Japan the leader country, Korea and TW as equal partners, then so on and so forth. So again, Pax America.
But the reality is China is in it. Biz-wise it's not out of the picture like Russia, rather it engages deep trade ties with all members of this region. Security-wise it's not like Germany, China's has its own geopolitical plans. So China is Russia + Germany? Or what is it? Sinosphere is more complicated than it seems, don't leave out the US factor. So the EU way (even with the magic formula you suggested) can't apply.
Further more on your magic formula, addition of India, doesn't solve the problem. I don't undermine India's weight, I do appreciate them as an important country, but the China to India weight ratio is a lot different from the Germany to UK weight ratio. Also, bringing India alone into the picture is incomplete, you should consider bringing the whole S Asia into this. But then I think the whole big game is so complicated that at least I can't figure out how to play with, worth exploring though.
Its an interesting and worthy point of conjecture tho -- to consider the plausibility of greater integration of South Asian - ASEAN - East Asia. Definitely would require us to read more into its strategic depth.