Patch panel woes

Hey guys, hoping someone with a little more layer 1 experience can point me in the right direction here.

I'm a cloud guy most of the time, but I need to wire up a few patch panels; a total of 136 RJ45s. I don't mind punching cat6 down into the panels, but I really don't want to put that many rj45s on that many cables. I've had bad experiences doing that in the past.

I was thinking I'd just buy a bunch of standard ethernet cables with the rj45s already on them, cut them all in half, cut them to length, and patch them in that way. But all the ones I find are stranded. My understanding is that you can't really punch down stranded cables, and if you do, the contact will be iffy at best.

I've been scouring Google trying to find premade solid core ethernet cables, and coming up short. The only place I could find that will get me what I want is showmecables.com, but they'd be quite expensive.

I only need to go ~7ft from the back of the panel, and only ~100 of the 136 jacks will be populated.

Does anyone know if/where I can find solid core, 14-ish foot, ethernet cables? Or 7' "whips" with an rj45 on just one end?