food safety in nearly-full crockpot?

I'm making "cassoulet" – it's not, really, even though I've added some duck, but I wanted comfort food. https://spicedblog.com/thomas-kellers-slow-cooker-cassoulet/

The crockpot is full to the brim, to the point that I actually had to take a cup or so of liquid off after a couple hours to keep it from overflowing. I put in pork sausages along with the duck, and the sausages have floated up to the top which is not surprising.

It's been cooking for about three hours now, on low, and while it is steaming and I can smell it from my home office, I'm wondering if it's possible to fill a slow cooker so full that the center just doesn't cook enough? I do go downstairs and stir it when I need to move around, but is it really going to get hot enough?

I don't have a meat thermometer, so can't measure the temp in the middle to see if it's getting above the danger-zone temp. But I'm not wild about incubating the world's largest bacterial culture in my kitchen…

ETA: I've now taken out half the duck and half the sausages. The ones I was fishing out of the center of the mess were not hot, so I'm glad I thought this through now rather than tomorrow when I got sick!