You would like to have:
cmd + .alt + (< | > | backspace)Before we begin let’s ensure we have iterm2:
brew cask install iterm2
Let’s address remaining issues in step by step approach:
cmd + .open iterm2
open preferences
cmd + ,
head to keys tab
click Create a dedicated Hotkey Window
add hotkey cmd + .
check option of floating window

fullscreen, screen = screen with cursor, space = all spaces
Result:

alt + (< | > | backspace)iTerm > Preferences > Profiles > Keys: