Teddy is a genius!
I was struggling with the exact same situation. No matter how much I deleted off my Hard Drive - it didn’t affect the free space listed in the installer.
I also moved the installer to an external HD and still no luck.
Trying Teddy’s method, disabling Time Machine and then using Terminal to remove the snapshots worked a treat. Suddenly the free space required on the installer was dropping and allowed me to install onto Macintosh HD! Thanks for your help.