I realised that passing a http client using SolrNetOptions is being ignored completely in Solrnet, so I don't think it's possible to change timeout value.
However, my problem was that I was trying to speed up bulk indexing using Parallel.ForEach and indexing chunk sizes of 2000 documents (using AddRangeAsync) which did "bombard" Solr with requests and Solr couldn't handle them. I kept getting "Early EOF exceptions"
So in case someone else is having the same problem, my solution was that I needed to throttle Parallel.ForEach by setting a value of MaxDegreeOfParallelism (in my case value 5 worked out quite well but you'll need to test for yourself as this can differ depending on what machine you're working on) and using ".Wait()" inside my Parallel.Foreach loop where I called my "AddRangeAsync" method so that it would wait for Solr to index the chunk before it would feed Solr with more chunks.
This just as information, I hope it might help anyone running into the same problem I did.