Let me say this from the get-go I know nothing about Allisons Transmissions.
That said and reading some of the thoughtful ideas on what to look for? as to the cooler being the issue? Let me say this my 2001 F350 diesel uses a trans cooler bypass so that when the coolant is cold it by-passes the transmission cooler until the fluid reaches a specific temperature then opens and allows the fluid to pass thu the trans oil cooler to then do its job.
In the light-duty vehicle world, they use these transmission oil cooler bypass valves in many applications and manufactures... and they have been known to fail and when doing so they can be very hard to diagnose ..especially if it is sticking intermittently because the trans isn't running hot at al times
As to flushing your trans oil cooler?
If the cooler type is a continuous serpentine loop meaning one continuous line in the cooler and is the same continual line coming out .....flushing the cooler is is fine if done properly. If your cooler is what I refer to as a manifold type meaning the trans fluid goes in one side or end of the trans cooler tank and the fluid can randomly go thu any of the cooling tubes and out the other end? and you have had a catastrophic trans failure you will never get it clean unless disassembled or replace it.
Seen here is a pic of one example of a transmission oil cooler by-pass from a Ford transmission and like I said many manufacturers use some sort of ny-pass to get the fluid up optimum operating temperature quickly.
I to believe that from what you report here that the trans failure is due to something else such as a high fluid temp issue or electrical issue.
IMO you need a schematic of your transmission that covers from from A to Z and examine it very closely.
I also think that if it was severely overheated trans that a seasoned trans tech would have reported that to you or the service advisor ...these folks do this day in and day out and most failures they are failed components and not severely overheated and when seeing a severely overheat trans that would normally send their diagnostics antenna's thu the roof and start question things.
I feel your pain with your tranny issue and wish you well with both your coach and your health.
Happy Trails.