Yes, definitely the reboot will restart all the processes, however have you rebooted the device after the first reboot that lead to the j-web failure?
Regarding the version, for some reason is no longer showing under Juniper page for download, however I found this link to get it,
https://webdownload.juniper.net/swdl/dl/secure/site/1/record/79745.html
The procedure will be like a normal upgrade, copy the image to /var/tmp/ and then delete the old image and install the new one,
> request system software delete jweb
> request system software add /var/tmp/....
Please mark as "Solved" if this works for you so we can help others too 🙂
Regards,
Jeff