well, first I admit that it is great thread.
OT: you are correct on the most part but not completly. Sage of six paths didnt seal his soul/ chakra avatar/imprint or whatever among all his powers in kurama because then tailed beasts other then kurama entrusting their souls along with a bit of their chakra would be pointless action and it had too great impact on the plot to be skipped just easily.
Of course Kurama is special case but it could be due to being the wisest among beasts created by Sage of six paths. Sage most likely noticed it so he divide himself in nine parts then sealed them among all tailed beasts. However noone know that Sage didn't divide himself in nine equal parts but differently in amount of his powers and chakra.
Kurama for being the strongest got the most of Sage's essense, most likely directly proportional to amount of his tails or mind. Gyuuki got big part but much smaller and rest beasts got respective amount of Sage's essense directly proportional to amout of tails they had.
The reason why Kurama was favourized by Sage could be that Kurama was the wisest and would be the hardest to be convinced so for reaching such feat Sage wanted to award someone so high. It could be also reason why Kurama hosts are only one to manifests Sage's appearance due to having so big amount of chakra from Sage. Most likely Gyuuki has too little to manifest it so other beasts.
However Sage as being wise man still ensured that you need to get trust from ALL Tailed beasts, even the weakest to meet him and get his help/ powers. Yes even the small amount of Sage's essence sealed in the weakest beast was priceless to complete requirements for Meeting Sage.
These are my thoughts
