How can I troubleshoot the slowness?

[bitmap]

Yes an SSD will absolutely make a difference. however, those times are pretty high so it may not be a panacea for your issues. Even on crap internet with a solid signal it only takes several seconds for my home page to load when I'm remote. As for local/networked storage: there will always be a difference (read: increase in latency) when moving from locally-attached storage to network-attached storage. And with Kodi, it generally loads up a file index rather than a "streaming" experience.

You can post your Jellyfin log to privatebin.net if you want help taking a look, but it doesn't sound like errors are the issue. One more question: are your server (i.e., your NAS) and clients using WiFi?