Here's a patch that applies on branch_6x. It required a different approach than master because 6.x uses an older deprecated http client API. I ended up extending DefaultHttpClient to override the createRequestExecutor() method which creates and sets up the InstrumentedHttpRequestExecutor.
This does not use the HttpClientFactory and its methods introduced in
SOLR-6625 but firstly the factory's static setter is never used in Solr and secondly, I'll open an issue to get rid of it completely.