Try not to focus on the gross misconduct as explaining the circumstances if they are as you outline will probably get you a little bit of sympathy. Try and get a 30-second pitch on what happened, nail it up front in an interview get it out the way.
"Allow me to explain my current situation. I had decided to leave my current employer for several reasons, not least the fact my hard work and commitment was not being rewards and that I had struggled to take any holiday or even get it approved for over X months. Because of this, I had embarked on a number of interviews most in my own time, but one company was insistent on a time during my work week. I decided this was a significant opportunity so I took the only false sickness day of my work life, something I now regret. I was asked by a confidant how it went and foolishly I was overheard, it was escalated and now I am here. A lesson learnt but an example of why I feel a new career move was vital as I want to a commit to a company that values its people and offers me an opportunity to build a career." etc.
Put it out there, be clear in your view and move on.
"Allow me to explain my current situation. I had decided to leave my current employer for several reasons, not least the fact my hard work and commitment was not being rewards and that I had struggled to take any holiday or even get it approved for over X months. Because of this, I had embarked on a number of interviews most in my own time, but one company was insistent on a time during my work week. I decided this was a significant opportunity so I took the only false sickness day of my work life, something I now regret. I was asked by a confidant how it went and foolishly I was overheard, it was escalated and now I am here. A lesson learnt but an example of why I feel a new career move was vital as I want to a commit to a company that values its people and offers me an opportunity to build a career." etc.
Put it out there, be clear in your view and move on.