Certificate in use was created using only a Common Name on the subject, all other subject fields were blank.
This was causing issues with the TCP connection, and the SRX sent TCP RSTs to the host when attempting to initiate a J-Web connection.
We created a new certificate with Common Name, Organization, Locality and Country on the subject, added IP address and ca-constraint. Replaced the previous certificate with this one and attempted to connect to J-Web once again. J-Web was accessible afterwards.