In case someone comes to this post in the future, I determined that it's probably frost damage.

Your roses look to be about 1/2 dead at this time. The watering for container roses is insufficient for newly planted bare roots. If the containers have good drainage, you should be watering them about 2-3 times a week. You say you used a 2:1 mix of potting soil and perlite. Potting soil should be planting mix and less of the perlite, if any. Roses need a sandy loam growing environment. Potting mix is for houseplants, not garden plants. Cut off the dead ends of the bushes with sharp bypass shears to 1/4 inch about the new growth or a burgundy bud-eye. The cane damage is canker dieback and is often found on bare roots that are stressed for water. The ceramic containers are about the right size, I think. They should be about 24" x 24" by 30" deep for a large rose to grow to mature size in two years. Rose bushes are frost-tolerant; immature rose leaves and blooms are not. Remove any damaged leafsets. If possible the roses need to be in rising sun until about 12N in the summer then can be shaded from the afternoon sun. Roses need at least 4-6 hours of early sun in order to thrive. Too much sun and they'll bake in the container. Too little sun and they'll have twiggy growth without much bloom. Hope this information helps, Jeannie Cochell, Master Rosarian, Phoenix Rose Society

Don't be too hard on yourself. I used to buy bare-root roses, but I had such iffy results with them, I quit buying them.

I'd recommend you buy small, potted growing roses from Lowes (they even sell discounted ones in the clearance section that have turned out fine for me.)

The problem with bare root roses is that the plants are dormant and the roots have no root hairs, so basically they have little ability to absorb nutrients and moisture until the roots start growing root hairs. Potted roses don't have this limitation, since they're not dormant. Best way to plant bare root roses is to cover the entire plant (including the canes) in moist soil, kept moist, until the stems show growth, then pull back the soil surrounding the canes. Leave the graft above ground.

Thank you Jeannie and Doug for the advice! I really appreciate your suggestions. Since I posted, I removed the damaged leaves and increased watering to twice a week and the roses seem to have responded well to that, although still not great. I'll bump it up to 3 x watering per week and cut back the canker. I could repot them in sandy loam if that's a good idea at this point. Unfortunately, they're stuck in their location of not getting early morning sun. So I'll just keep at it and if they die, I'll switch to trying potted roses.

Good. It's time for the roses to be covered in new leaves and stems. To make sure your roses are getting ample water in the pots, you can use a moisture meter. They're fairly cheap and easily available. You can also increase the moisture retention by mulching the containers. As these roses are already stressed I wouldn't encourage any digging around in the roots right now or repotting them in a different medium. Hardy roses will grow. Diva roses will succumb.