You could try detangling in the shower with the conditioner still own. You will see a lot of posts talking about conditioner with SLIP. Slip means how easy the comb slips through your hair when you detangle. If you can find a conditioner with good slip you will save a lot of hair.
I take the time to also detangle or rather finger comb before I co-wash and apply oil on it almost like an oil rinse before hand and let it sit for like 15mins with a shower cap for the body heat. Then I do as you with detangling in sections but detangle with conditioner on it also from the ends up.
HTH
Just take your time and don't fret.
Howdy!!! My hair was damp when I detangled. I believe your are right about needing moisture. My hair has been extremely dry lately but that's from me being lazy.Just based on what you said, it sounds like you should focus on getting moisture into your hair. Was your hair dry when you combed? If so, try to refrain from detangling dry hair. Get you a good detangler - I hear Mane & Tal makes a good one.
My #1 recommedation/solution: MOISTURE
HTH!
Can't remember where I saw it (maybe www.healthyhairjourney.com ) but one of the things this lady does is comb and part her hair in 4 sections and shampoo each section at a time. Immediately puting the hair back up and moving on to the next section.
I did this the last time I shampooed due to all the shedding I was having and I was very pleased with the results.
There is no tangling because you're only working with small sections at a time if this makes any sense. Try it and I'm sure you'll be pleased, I was.