All of your advice is 100% correct. And I've been doing it for years, with every phone I have. I took a break from CS in 2019, when the game worked reasonably well (except during Weekday Warrior where it would get a bit overwhelmed by all the clicks and loot.)
But right now the game pauses every time I click something, like it's super-overloaded.
My phone isn't terribly old - Motorola z2 force was a flagship model circa 2016. And I recently did a factory data wipe, so I don't have a lot of congestion. 32Gb of onboard memory plus 32 Gb SD card, each only half full of my old files. VERY few apps.
Castle Story cache is 90kb but storage is 1.4 Gb. That seemed high so I cleared them, but after taking a zillion years to load (my normal load time in 2021 is 2 minutes), the movement pauses quickly kick in again.
Maybe I should reinstall, but SW said that was only for graphics issues.
EDIT: just wiped data and cache, we'll see how it goes