I do have to ask - why don't you want to use SSR just because it's an internal application? For the new Svelte Society website we're SSR:ing everything (even the Admin dashboard). Being able to use form actions is a god send.
With that said, unfortunately when using Kit in "SPA mode" you're not getting the full experience, but it's still the best thing out there. You could try Routify as well.
There's a great talk from last years Svelte Summit that was about Svelte(Kit) in "SPA mode".
https://www.youtube.com/watch?v=uIZOeBS-3cI
TL;DR: Lean into load functions and monkey-patch fetch (if possible)