I recently had a few cuttings root in the bottom of styro cups filled with a light potting mix similar to yours. The ones that were two to a cup I VERY carefully separated and put in separate cups, with about an inch more dirt under the roots. Using advice from Roseseek, I'm going to tip them out of the cups about once a week and add more dirt under the roots, so they gradually have more stem above ground and more room to grow roots. I may be going a bit slow on this, but these are my first babies and I am being extra careful.

I don't know if you can tip your new roses out of the plastic cartons as easily as I can from the styro cups. I tried tipping out the (dead) cuttings in my plastic milk cartons and didn't have much success. I don't know if milk cartons are "less slidey" or if it was because they had no roots to hold the soil.

Milk cartons are a pretty good size, bigger than the bands that are shipped to me with well branched roses. I expect you could leave them in there for "a while," at least until you see a good number of roots in the bottom of the milk carton.

I can't remember from your post, but do you have drainage holes in your milk cartons? They are pretty necessary for your cuttings to continue growing.

I'd give them more time before you try and repot them. What roots they have at 3 weeks are very small and you don't want to damage them. You should be able to see roots through the milk jug so you'll know if they start to look too root bound and need potting up.

So the milk carton was a good and bad idea. Bad, more than one in each. Good, I can see the roots. I haven't even looked underneath! I can support them until I see some real roots.
What are bands? I am not a rosarian, but do like roses, and they do well here.
I was looking for an Annie Laurie McDowell, but haven't been able to find one yet.

Bands, that I have received, are young/small roses growing in 5" deep narrow pots that I have seen described as the pots used to grow tree seedlings. I popped mine directly in the prepared soil. They came from Heirloom Roses and they grew terrific last year, even with the dry weather around here. Bands are smaller and cost less to ship than gallons.

Help Me Find says Burlington Roses sells Annie Laurie McDowell. Maybe you could contact her to see if the rose is available.

Here is a link that might be useful: Burlington Roses

Wow. That was easy enough!

No roots showing yet.

They are growing! Amazing.

It is exciting to see leaves growing! Sounds like you have the cuttings in a good spot for light to grow the leaves. The more important things that need to grow are roots. Be patient with the cuttings and NO TUGGING to see if they are rooting. Watch for your roots to show up along the wall of the milk jug. Hope your Lady Banks roots well!