I don’t have crossbars and I’m not sure I want them. Has anyone come across rod holders that would clip to the front and rear of one of the roof rack rails?
Honestly, I usually use some Velcro straps and thin dense foam pieces. The foam is just there to avoid rubbing - it's really thin. (I have a lot of saltwater rigs that don't fit inside, so rods outside is normal for me.)
It's not the prettiest, but it only takes a minute to put on/off and it's been perfectly secure even on long interstate trips.
I have a roof platform now, but I use the same approach for rods on the underside of it that I did on the top of the side rails before I had the platform. It's easier to leave reels on with the platform, though. They can hang down without touching anything. I wouldn't do that with only the side rails.
I've looked quite a bit at rod holders and eventually decided that simpler is better. I haven't seen anything quite like what you're wanting, though. The side rails are more curved than they look at first, btw. You can't easily fit something rigid down their length due to the curve. Otherwise, I'd suggest trying a homemade pvc carrier.