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Thanks for the help investigating this. We've identified a possible race condition during initialization, specifically involving discovering the connection string of the currently installed instance.
The presence of .NET 2 shouldn't affect things, as the installer specifically targets 4. The 20 in the CLR20 error just refers to the runtime version. .NET 4 runs on the CLR 2.0 runtime, confusingly enough.
We've made a small code change which should resolve this issue - assuming it is the cause. We haven't been able to reproduce it on our systems. The installer for the next version (which should be 3.6.2) will have the fix, so you may want to try using the larger installer again just to see if the issue goes away. You never need the full installer to perform an upgrade, however.
Again, thanks for the help!