I think you're a wild card. In other words, it's going to be hard to predict at all because it'll come down to the individual adcoms reading your case, and my hunch is that there very well could be debate (your applications at each school are read by at least 2 different adcoms members). Most of the PhD folks they see are in life sciences or engineering, so with your background they won't really know what to do with you. It's not about whether you have finance experience or not (the majority of applicants do not) but the fact that they rarely if ever get someone with your background. So your challenge isn't "standing out" but whether the adcoms believe that you can "fit in" with a sea of ex-bankers, consultants, engineers, and other corporate professionals. It also doesn't help that your goals are also atypical (not saying you should say something else, because if you decide to go with the more standard narrative of management consulting or corporate, it will be a different kind of hard sell because you'll have to convince them that you can transition into the corporate world which is likely very different than your experiences to date). Finally, if you get into b-school, are you going to drop out of the PhD program? Keep in mind that by applying to b-school, it sends a strong signal that you feel you made a huge mistake doing this PhD and you're scrambling to right the ship so to speak by applying to another program. And yes, all of what I said here doesn't just apply to HBS or Stanford, or even Wharton, Columbia, etc. but any top b-school you'll be looking at.
In any case, if you need to scratch that itch, then by all means apply. But I strongly suggest you look for work (I know the job market sucks) while you're doing your PhD program - and if you land a good job, consider either dropping the PhD program or going part-time with it if at all possible.