Well, I found myself with the same problem as these reported bugs:
ID: 3400623
ID: 3039968
I have downloaded the code and start to dig on it. It seems that both MapperAware and ConfigurableCustomConverter introduce this undessire behaviour.
What I did (I am submitting a patch) was:
* Remove those both interfaces
* Added Mapper and Parameters as part of the public convert method of CustomConverter.
* Modified MappingProcessor.mapUsingCustomConverterInstance to pass through this new variables as method parameters.
This will obviously push to some code changes on client customerConverters, but will avoid the concurrency problem.
See the file attached, I worked on trunk version but I feel it might be compatible with 5.3.2
Patch