What you're saying makes a lot of sense to me. Unfortunately, we may need to make a decision here before we really know whether it's short-term or long-term burnout, because we have to decide pretty-much-100% whether and when I'm going to be back, before I take my break. If there's too much uncertainty, it's a no-go.
If we had the stability to simply put things on hold, I would definitely take 6-8 weeks off before we decided what to do.
At the end of the two months, I have to say, the old job didn't sound so bad anymore. I started grad school afterwards, so I was charged up, but I suspect that the time off was what I really needed. Looking back, it was actually one of the more innovative startups I've ever worked at.
You may be looking at deep long term burnout, but how long as it been since you've walked away from work long enough to reset your head? It doesn't have to be decades - a single year of 10 hour days where you often find yourself at the office on weekends can be enough to cause your mind to rebel and shut down. Think of your head as an employee that has been pushed too hard, and has retaliated by not producing anything.
I've learned to identify my short-term tendency to burn out and distinguish it from true career malaise. Maybe I just need more time off than the average person. I wish I could drive harder, but if I can't, I may as well know that about myself and minimize the damage.