I would not say that your flow is globally unstable. Considering LES with no artificial turbulence generated at inlets, I would expect to obtain delayed turbulence structures. However, if you say that you are satisfied with the results given by this model, I imagine that it is more suitable than it seems.
In regards to your problem, you have said that your configuration is 2m pipe RANS + 0.5 m LES. What happens if you consider 1 m RANS sand 1.5 m LES? And if 0.5 m RANS and 2 m LES? Checking what happens when l_RANS ->0 can be interesting.