EFC: welcome to the forum! I have to echo the above... and let you also know that you and I are in the same boat!
I am a year and a half older than you. I have the same life experiences as you (for the most part, but without the children): college degree and cooresponding loan for same. A mortgage. I'm married (very recently so) and I am working on my private certificate en route to a career in aviation.
Medically, I had some cardio exams done about two years ago (which, like you, came up negative). I put that on my Med/Student Pilot App and had no problem because the results were negative.
The long and short to this post is to say: YES - from everything I've read, researched and learned through word of mouth - it is indeed both possible and done quite frequently. It had better be - I've bankrolled a good deal of cash in hopes of getting to where I want to go.
Bottom line: Don't let anyone - ANYONE tell you that you cannot do it!!! You can. You're way ahead of me already.
Good luck and if you have any quesitons, drop me a line on my Private Message section or my e-mail:
shayes@fowlerwhite.com
Take care!
r2f