How can I sleep computer AND lock screen with a shortcut, but not after screensaver starts?

Running Mojave (10.14.6), I want to be able to issue a single keyboard shortcut that will immediately put the computer to sleep such that (a) displays are off immediately and (b) a password will be required, even after less than a minute. However, I *also* want a password to *not* be required immediately if the screensaver is activated by the computer sitting idle. (Call this requirement #2.) What I've tried: 1. Setting "start screensaver after" to 5 minutes and "require password ___ after sleep or screensaver begins" to 5 minutes as well. This solves requirement 2 but not requirement 1. 2. Issuing the "sleep" command in Alfred. This puts the display to sleep but doesn't require password immediately after. 3. Issuing the "lock" command in Alfred. This requires password immediately but doesn't put the display to sleep. 4. Using the "sleep computer" action in BetterTouchTool. This works exactly like its counterpart in Alfred; no password is required if the computer is woken immediately. 5. Using the "lock screen" action in BTT. This isn't working for me at all.