First, don’t be so quick to dismiss Rorty, for he possibly provides the bridge between continental and analytic philosophy that you’re looking for. At the risk of oversimplification, Rorty’s thesis in his opus, Contingency, Irony and Solidarity, is that “striving to get things right” is still a worthwhile pursuit, made all the more valuable when we admit that there is no “right.” Our commitments to values like liberalism, democracy, etc. are in fact made stronger when we choose them because we feel they’re the best way to conduct our affairs, as opposed to choose them because they’re analytically sensible. To be a little crass, people seldom put their lives on the line for a formula or equation (not to suggest that analytic philosophy is simply math with words, although some of it is), whereas countless men and women die every day for beliefs.
This brings me to my second point. You say the goal of philosophy is to help potential be realized. I doubt many would dispute this point, but what’s up for debate is how best to achieve this goal. What many, including Rorty, would suggest is that people are mobilized more by stories, myths, drama, etc. than by rational arguments. Personally, I think this becomes more evident with every passing day, but sadly, it is the so-called Right that has clued into this. It’s an increasingly common critique of the contemporary, visible and popular left that they’ve failed to win over the hearts and minds of the people because they’ve adhered to the notion, as Barthes put it, that the left does not need myth because it has truth on its side. Tell that to the people who believe, despite concrete evidence to the contrary, that Obama was born in Kenya… So, essentially, if you want to “realize potential,” you may need to accept that the continental approach to doing so is the better method (at least at this moment).
In closing, I’d be wary of setting up this binary between analytic and continental philosophy, that while useful for your purposes, may not stand to real scrutiny. For every analytic philosopher who transcends simply “spotting weakness” there is a continental philosopher possessed of strong, clear argumentation (Rorty being one of them). There should never be a “one best way” of doing philosophy, and in many ways, that is precisely what the continental tradition is reacting against. Nor should all philosophy necessarily need to be timeless and eternal. Far more generative is philosophy that is contextually appropriate to its era, and thus allows those living in that era to better understand their time.
tl;dr All hail nuance! Contest precisely those ideas that go uncontested! Or something like that…
I think you are quite right to point out the significance of feelings in doing philosophy. Our feelings and beliefs play a powerful role in forming what philosophers call ‘our pre-philosophical intuitions.’ Despite first appearances, the dominant trend in contemporary ethics is not Rawlsian thought-experiments or abstract utilitarian moral calculus, but a way of doing ethics that is based around our intuitions. It involves examining our thoughts and feelings about a moral issue carefully, then seeing which of our intuitions are well-grounded. If they are, then we can figure out which moral principles motivate (or ought to motivate) our intuitions so the principles can be applied to other relevant situations. A lot of very good analytic philosophy has been done that gives our feelings and intuitions the respect and careful thought they deserve.
As a realist, however, I feel obligated to dismiss Rorty’s idea that ‘there is no right.’ It’s difficult to understand Rorty’s denial of realism given that he was a pragmatist- after all, how can we do what works without an epistemically and ontologically objective world in which to work? As John Searle writes, it’s difficult to give an argument for the external world or a correspondence theory of truth, as these are often presupposed even by philosophers who attempt to deny them. Searle’s version of realism stresses that there can be multiple valid ways of interpreting the same world (a notion that I have no intention of denying), an idea he calls ‘conceptual relativity.’ But Searle also says it does not follow from the truth of this that realism is false, there is no such thing as truth, or that reality is merely a social construct, and contends that it is a category error to assume so, as I believe Rorty does.