How to end the game in 2-player Lemmings (Super Nintendo), with no "Nuke" option?

I'm sharing my old SNES games with my kids and we were trying out the 2-player mode on Lemmings.

Sadly, it seems you can get into the situation where someone has used all of their "Bombers" and still have "Blockers" left that aren't able to be saved - leaving the 2-player game stuck with no way to keep playing without resetting the console.

In 1-player mode, there are three ways to get out of this situation:

1. Hold SELECT and Press START
2. Use the "Mushroom Cloud" button to "Nuke" all the Lemmings
3. Wait for the timer to run out.

Here is a screenshot of the second option in 1-player mode. Notice the "Mushroom Cloud" in the bottom center of the image (Next to the yellow highlighted "Digger" box):

Unfortunately, in 2-player mode the SELECT + START method doesn't seem to work - even if both players do it simultaneously. That leaves the other two options, but with no timer and no "Nuke" option on the screen, it seems that it is impossible to end the round and keep playing when you get into this situation.

Here is a screenshot showing the lack of a "mushroom cloud" button in 2-player mode:

We no longer have the game manual, but surely there should be a way to continue playing the game in those situations? Being forced to reset the console is most disappointing.