Oh, I feel you.
DS's first four months were absolutely hellish for car rides. I really don't know what she hated about the carseat so much, but now at 5 months, she is doing A LOT better....
Some things that we had success with:
The pacifier. I know you said you don't really use them, but they were pretty much a lifesaver on some trips. When she was a newborn, one of us often sat in the backseat and actually held the pacifier in since she wasn't very successful at keeping it in herself. Could one of your older children reach LO#4 to help hold the paci in?
Putting her in the carseat just after she had fallen asleep. this one took a lot of planning in advance. We would get the car loaded with bag and whatever else we were taking, get DS in (he's 3) start the car, and then wait for her to drift off. Ever so gently, I'd place her in the carseat and tighten the straps ridiculously slowly so as not to wake her up. Then carry the carseat out to the car and go. This worked pretty well most of the time. She would take a regular length nap while the car was running, so it was good for a hour or so trip.
We did what we jokingly called "conditioning" at times. When I would put her into the carseat initially, I would smile excessively, talk super sweet talk, and try to be insanely happy/give her positive vibes about the carseat. I'd spend a good 5 or 10 minutesgiving her lots of love while she sat in the carseat... and then bring her out to the car.
Putting something into her hands, even when she was a newborn/infant seemed to help. As soon as she could grasp, I would put one of those plastic play rings in each of her hands before we started driving. She would grip them for most of the trip.
Now at 4 and 5 months, plastic rings hanging from the carseat handle are pretty much what keeps her happy and entertained. (i know, they aren't recommended for use while driving, but....)
I totally hear where you are coming from on the crying. I often stopped and held her or nursed if she started crying. It took us forever to get places sometimes, too. for the sake of practicality, I try to tough out about 5 minutes of crying. I can't in good conscience let it go longer than that. But to be realistic, I do let her fuss/cry for a bit if I know I am just a few more minutes from our destination. Especially since I know I'm going to get her out of the car as soon as we get there and hold her.... Hope that helps some....