I am very happy that you are seeing progress and am grateful that you are sharing in detail the 301 case study. A thread like this is a like a shred of light.
I however think you are being wrong by saying your site has very clean backlink profile. As we all know 301 transfers all of the link juice from old pages to the ones of the new site. With this being said, yes your site has now a clean profile, but in few weeks when the process of transferring is complete, all old links will be carried out to the new site.
So my assumption is that the chronology of such a trial will go:
1. Immediaate relief with the 301 as its practically a new site
2. Short boost of some pages as there is not even a sandbox during the first 10-15 days on newly launched sites. This in combination with the 301 adds up
3. Old Links being carried over to the new pages (possibly old penalties as well)
4. Site is being reassesed with all major algos once all data is being transferred (Penguin, Panda etc)
5. SERPS being updated after all algos are done
If you go through 1-5 without losing your SERPS again its likely that the on-page changes that you've made could have solved the problem and not the 301. The 301 can theoretically speed up the whole process.
I hope this is not discouraging, It's my pure assumption. Please keep us updated. I hope I am wrong and I am crossing my fingers for you mate.
All I know is my old site is gone and I have a brand new clean site with content that has been deopitmized and a very clean backlink profile which I'm building slowly using different methods.