If it is standalone and only Essbase personally I see no point in patching and then upgrading to 184.108.40.206, I would prefer to have a clean install and then migrate the application as if you moving to 220.127.116.11 then no doubt it will be new hardware and OS.
One possible method would be to install and configure 18.104.22.168 then use the EAS migration wizard to migrate the Essbase applications, data would need to be migrated separated.
You would also need to consider security if you are moving to Shared Services security in 22.214.171.124
It may be worth discussing your options with a consultant as there important points that should be covered which is probably not for a forum.,
You said "if" I am moving to Shared Servies Security Mode. I thought I had to. I was thinking of going the maxL export/import route (https://forums.oracle.com/thread/2445953) along with the EAS Migration Wizard. Thought I needed the relational backend just to get HSS/EAS/ESB installed and to start the Agent.
This business unit uses Essbase/EAS/Add-In only. (Others here use HFM/Planning or a combination thereof). So this one's a D.I.Y.. Would my plan above get me something that at least works?
Just one last question; extracting the security info with maxL/display from 9.3.1 and and manufacturing the maxL creates and grants and running those in the 126.96.36.199 Shared Servies mode environment could be a workable "migration"? (once the apps/databases etc. are wizard-ed from 9.3.1 to 188.8.131.52?)