Imho bidirectional replication is very very far from 'it will just work'. Preventing update conflicts requires exquisite planning, ensuring that all that 'processing' is carefully orchestrated never to work on overlapping data. Master-master replication is one of the most difficult solution to pull off.
Consider this: you envision a solution that is providing a cheap 2x scale out with nearly no code modification. such a solution would be quite useful, one would expect to see it deployed everywhere. Yet is nowhere to be seen.
I recommend you search for the many blogs and articles describing gotchas and warnings about (the much more popular) MySQL master-master deployments (eg. If You Must Deploy Multi-Master Replication, Read This First), judge for yourself is the trouble is worth it.
I don't have all the details you do, but I would focus on the application. If you want to just throw money at the problem short term I would make sure that the cheap scale-up is exhausted before considering scale-out (SSD/Fusion drives, more RAM). Also investigate snapshot isolation level/read committed snapshot first, if locking is the main issue.