I don't think that this is possible with HDFS. Even though you don't care about the order of the records, you do care about the order of the bytes in the file. You don't want writer A to write a partial record that then gets corrupted by writer B. This is a hard problem for HDFS to solve on its own, so it doesn't.
Create a file per writer. Pass all the files to any MapReduce worker that needs to read this data. This is much simpler and fits the design of HDFS and Hadoop. If non-MapReduce code needs to read this data as one stream then either stream each file sequentially or write a very quick MapReduce job to consolidate the files.
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