I'd leave them in the ground if possible and just untangle them from the fence. Cut them back if need be. This is not a great time for transplantation and they may not survive.
If you have to take them out, your plan is probably the best you can do. Make sure to keep the roots wet the entire time they're out. That's going to be your main killer.
I think being stepped on would be less trauma than transplanting. You could always fold them back onto your property and wrap them with some flagging tape or something to keep them visible to workers.
By cutting them back, I meant cutting them back to a reasonable length to manage. It's usually not great to prune plants more than 1/3 of their total size, but some plants will even recover from a full cut back. The jasmine will be fine. Depending on the rose variety, they should be ok too. Some people seriously prune roses to encourage flowering.