I think you absolutely can find a position that fulfills your requirements (mainly because I have one like that and love it!), however it's either going to take just getting lucky and striking gold randomly, or networking like crazy with your network and having them tell you about what the work atmosphere at their office is like and back channeling you with their HR. Great companies with great work cultures exist, but they're like exclusive rent control apartments... we tend to fill openings with internal referrals because the talent brings their best colleagues from their previous jobs.

How I got into where I am was I dumb-lucked into it by connecting with a great recruiter and randomly having the hiring team like me a lot. I've been there two years and have recruited two of my best previous coworkers from other jobs to come join us. We are all loving life.

Anyways... work your network! Good luck and don't give up!! I would say stay away from newbie startups and go to midsize profitable firms.

edit: I don't have my own private office, but I have a really big high walled private cube with a door. big enough to leave my bike inside it and do yoga inside. I love it. I feel dorky in a cube but it is really nice!