I was experiencing the same problem:
So my work around was:
Step 1: Solr path config - enter :/solr/. This caused the SOLR and Drupal to be able to communicate.
However, the index fails because the URL cannot be used for the httpPost or httpGet. The following error will surface: SearchApiException while deleting items from server : "400" Status: HTTP method POST is not supported by this URL: HTTP method POST is not supported by this URL
Step 2: Remove '#/~cores/'
The correct URI is the path listed in SOLR w/o the extra characters. Surprisingly, once I ran cron and restarted tomcat - the servers were still able to communicate and the index ran as designed.
NOTE: I had to delete the index configuration that failed and reconfigure AFTER making these changes. It seems there's some type of weird caching that 'remembers' the configuration ::shrug:::
Worked for me. And I hope it works for you. It took me a couple of hours to figure it out.