If only debt-ceiling debates went this smoothly.
But that would mean that the people doing the debates would have to love what they're talking about...
Anyways, we know that there was a process of linking up pilot and machine. Perhaps they gave her a stimulant, hooked her up to Eva and hoped that she would have regained her ability to synch to a point where she could move the Eva and escape. Perhaps that stimulant woke her up, and she was able to link to Eva, considering her mental breakdown also destroyed her ego, the very thing keeping her from synching because it closed off her heart. With this pride smashed, the little girl inside could reach out of the shell and beg for help, which stimulates Unit 02 to reach over and begin synching. This builds up until the Mother Epiphany can occur, which shocks her brain into consciousness.
Again, feeling pain from the Eva means that she's already in synch with it. In addition, consider the fact that Eva's plug is often referred to as a womb.
By the by, here's a quote from Diane Ackerman's Discoveries on Your Doorstep
"...The moment a newborn opens its eyes, discovery begins. I learned this with a laugh one morning after delivering a calf. When it lifted up its fluffy head and looked at me, its eyes held the absolute bewilderment of the newly born. A moment before it had enjoyed the even black nowhere of the womb, and suddenly its world was full of color, movement and noise. I've never seen anything so shocked to be alive."
While much of that passage is actually irrelevant to our discussion, it is important to see that the author mentions the shock of being born. Asuka was at least completely withdrawn, in "the even black nowhere" of her inner self (One can almost say her personal hell train car). Suddenly, she is presented with the fact that she is alive, a thought which then triggers a cascade of self-awareness. I believe that the bomb, along with a stimulant, may have woken her brain a little (and again I reiterate the fact that she was able to feel Eva's pain, an indication of partial synchronization), and that awakened portion gradually roused the rest of her mind. Stimulants may have helped. Since she no longer has her all-blocking AT Field-like-Ego binding her mind, she could fully embrace Kyoko, inside Unit 02's Core. Thus, the Epiphany moment occured and she woke up fully, not only physically but also about herself, her reason for living/fighting and why she doesn't really want to die, after all.
I suppose this is much more philosophizing and speculation than a discussion about the actual drugs used, but I'd like to point out that there are lots of thing that they could've used, all to the same result. The banana pack was probably to keep her alive, since she's obviously not in the mood to eat up.