The disgusting thing was, that after leaving us with this unholy mess the LEAN team just vanished to jump on its next victim.
If that's what happened, it has nothing to do with LEAN. It was just plain old fashioned Time & Motion study.
...making small mistakes or oversights, unusually for them, and it's because they've too much on their plate but are determined to meet the targets;
LEAN is supposed to eliminate those small errors, and make it easier to work at maximum efficiency without making errors. Incidentally, 'Human Factors' is a compulsory subject in civil aviation engineering these days. Without a pass you don't get your licence and you can't be appointed to a 'nominated' management position without further training in HF.
LEAN is done in-house by the people who actually do the work. The LEAN team is merely a facilitator, assisting the end users with the process. To have a team that is not accountable for the results of implementation is a mockery. It seems there was an objective - to reduce training course duration - but what were the KPIs? Were they met? How was performance (including that of the LEAN team) measured? You suggest (subjectively) that quality was reduced; can you put numbers to that and make a quantified, objective assessment? If you can,
then you're getting the hang of LEAN.
Still, its what you'd expect in a military environment. Given your role, where shop floor democracy isn't always a good idea, its very hard for the military to properly use techniques designed for the more relaxed civilian way of working. Not that you shouldn't try, of course.