Then just turn on the phase cloak. (I should have thought of this one years ago!)
If you can't fire while phased (which seems reasonable), then activate the cloak a split-second after firing torpedoes. If that's not enough time, then put the torpedoes on a delay. Make sure you blast your way out on the side of the asteroid opposite the position of the Romulan ship so they can't see you emerge. Then just sail out (whether the opening is actually large enough for you or not). The instant you emerge, turn off the cloak. Then contact the Romulans. "Oh, it seems we don't require your assistance after all. Yes, that is quite a small opening. We barely scraped through thanks to the skills of a gifted pilot. Anyway, have a nice day!
"Helm, warp three. Engage. And hurry."
There are probably several holes in this idea, but the fact is Picard wouldn't have done it anyway because he would have felt honor-bound to declare the situation to the Romulans.
The flaw is that firing or mining with explosives in such a way would likely collapse the chasm. The Romulans' sensors are obviously going to notice that happen. You're still emerging miraculously & using the phase cloak to do it