I had the same issues myself until I ended up dropping Phaser and using Pixijs (the rendering code used by Phaser) on its own and then writing a bit of code to only render the game in chunks. It seems like by default Pixijs (and this may have changed since I wrote my code) renders the whole scene no matter how large it is. Since I'm working on dwarf fortress type game, the game world has a lot going on and it crushed my game's performance and brought it to a halt. Since writing that chunking code I haven't had any performance problems that weren't my own doing.
tl;dr I would recommend checking out Pixijs on its own if you still want to use TypeScript (I recently converted my code from es6 to TypeScript a month or two ago and am in love love love).