Hi,
I wonder why you want to avoid EJBs, but that is your decision. You would simply need a single EJB @Stateless bean with an @Asynchronous annotated method that you can call via CDI to pass in the ExecutableJobsRunnable.
For one thing, this will only give you RequestScope and ApplicationScope. SessionScope however is a completely different area, cause EJB will only provide this for Stateful beans. I wonder why you rely on SessionScoped beans for Activiti. What is your Session in that case? After becoming asynchronous via a Timer, there is no longer an associated session.
Otherwise, feel free to just start the scopes and see if that works. I wonder how entity management and transactions will work out. Simply adding a JTA transaction manager does not give you container based transactions, cause in unmanaged threads, no container will open up a transaction neither commit or rollback.
Btw. to start your scopes, refer to DeltaSpike Container Ctrl which helps you to start scopes pretty easily, rather than directly using Weld. Otherwise you might be incompatible with other application servers.