I wouldn't cut anything off those roots. I'd just plant them straight into the garden immediately, especially if pots are likely to freeze in your area.

Hard to id from the slightly droopy flowers but probably some sort of L peryclimenum. Not L japonica or sempervirens.

Thanks floral. I can't put them in the ground because i don't have any. I garden in pots on a balcony. :) Anyhow, i can bring the pots (gallon) in for the winter or leave them out sitting on or buried in 10 gallon pots (can't use those bigger pots yet, they have morning glories in them - the heavenly blue has lots of buds but still waiting for the first flower).

I planted them as such and the leaves wilted and remain so after a week. Should i be trimming the vines or chopping the leaves off? I know the current scientific understanding is that trimming stems while transplanting is inhelpful but what if i have so little of the roots that it is closer to a cutting than a transplant?

Did you water them well? Apart from keeping the soil slightly damp, I'd leave them alone. They've had a shock. Honeysuckle leafs out very early so I imagine you'll see some new growth early next year.

yes, they are watered well. I will let them be and hope for the best.

Happy to report that long unbranched vine (pic 1 and 2) retained some if its leaves at the tip and the second one (pics 3 and 4) is green and appears to be trying to sprot some leaves after loosing the existing leaves.