If avoiding open-plan is a priority, I recommend you focus on negotiating for a remote work arrangement, rather than excluding good companies. My last two long-term engagements have been at Fortune 100 companies and I've worked remotely for both.
In the first case, I was the only remote employee in my business unit. I was hired because I had a high level of competency with a technology they were investing heavily in. When I first interviewed, they told me that the were only considering on-site, and that my rate was too high. So, they first hired an on-site employee at a lower rate, but he failed to deliver a working installation and the project got perilously behind schedule. When I re-approached them about two months later they were no longer hung up on my rate or request to work remote. It's worth noting that I took a gamble here and put in about 6 or 8 hours interview and follow-up process, after being told that remote was not an option, and then being given the initial "no". During the project, I did stop by their Silicon Valley campus for a few hours of meetings every month or two, which was probably 1% or less of my total billable hours.
In my current engagement, my entire team is remote, so it was a non-issue. The gig was secured for me by a recruiter who had previously contacted me about an on-site position, and I told her I was only considering remote (and followed up periodically).
Both of these positions had multiple technical screens which were very rigorous. Both resulted from initial contacts where I was given at least one "no". You can have a private office at any company if you negotiate for remote and set yourself up with the office you like (e.g. home, co-working, etc.)