I'm a rigger for the military, so I pack 360 ft canopies with lines larger than I've seen on any civilian rig. A couple things I can tell you are tension, tension, tension(!!!) and keeping your connector links even at your container.
Those are two things that massively help in preventing spaghetti. If your lines are always even, there should (theoretically) be no room for them to escape at any point. Takes some practice though.
Another thing that could help, based off what you said about your first stow is not pulling directly from where they come out of the bag. I'll try to explain this the best way I can.
Once you have a closed dbag, pull some tension on your lines. Ideally, they should still be nice and even. From here (let's say your first stow is on the left, just for shits and giggles) grab your lines in your right hand using the index finger and thumb, holding them directly over the center of where they come out of the bag. Now make your first stow, making sure you're holding those lines.
What it sounds like you might be doing is making that first stow and pulling some lines further into the stow than the rest of them. When I'm stowing my lines, I always pull tension after every stow. It ensures I don't have any extra loose lines that might cause a line over, but it also helps me keep them really clean.
It takes some practice, but you'll find a method that works for you. Sorry for the long comment, I like helping people learn to pack.
Tl;Dr: TENSION