Delay is probably worse - now you're further disassociating the effect of the action from the action itself, breaking the usual rule: if you change something, and don't like the effect, change it back.
There is a relatively short window where dual engine shutdown is unrecoverable. Once you have a bit of altitude (and these jets climb at 2000-3000fpm) you have time for a restart and as thrust comes back sink rate will decrease even on one engine.
My proposal is during this window if dual engine shutdown is commanded don't do it. Treat it like it is happening - show the EICAS message, give the alert, but don't actually do the shutdown until the window has passed. This gives the pilots 10 seconds of startle factor then a bit of time to flip the switch back on.
Single engine shutdown would still behave as today so sure if one engine eats a fan blade shut it down. Not that it matters, the engine computer is going to cut fuel in that case anyway.
Insert a delay only for shutting down the remaining engine and only for X seconds after transition to air mode. A delay that the fire handle overrides.
Just a tiny bit of insurance. There aren't any emergency scenarios at low altitude where engine shutdown works but pulling the fire handle does not. You are coming right back to land at the airport no matter what.
Shutting off both engines would display "ENG SHUTDOWN" in yellow text (caution) on the EICAS. If only one engine was shut down, it would say "ENG SHUTDOWN L" or "ENG SHUTDOWN R".
Any of these would trigger an unmistakable audible "BLEEP BLEEP BLEEP" to draw your attention to the screen so that you could see what the caution was. These messages are right next to the engine N1 indications anyway, so it would be immediately obvious that one or more of the engines was spooling down.
