What did I end up doing? Well, it's a long story.
I thought I'd take the "roast and puree" people's advice, so I shredded some carrots and half a butternut squash I had, mixed everything together with a little salt, pepper, and a tablespoon of melted butter, and roasted it at about 350 for over an hour. It tasted kind of hard and very carroty, but it was time for bed so I just put it away. I was very disappointed.
Today I had a yearning for ribeye steak with a side of tender roasted leeks. Hoping against hope, I mixed large chunks of leeks with the carrot/squash mash, peppered it, and put it in the oven at 500. I took the steak out of the fridge to come up to room temperature, came back out, mixed the veggies around a little, cooked the steak, let the steak sit for five minutes, and plated the veggies.
Fantastic. Creamy, oniony, and a little sweet. It was exactly right with my barebones steak, and better than anything I could have imagined carrots could be. The leeks toward the top of the dish had caramelized to Carb Lover-worthiness.
Thanks for the point in the right direction, although as usual I seem to have veered far off the original path.
A photo of my slightly overcooked (to me) steak, for the visually inclined. As you can see, red meat took center stage today.