Kyla ...
>>>Hmm. That all sounds very wise! However, training the rose up those trees is kind of beyond my capacity (plus which the trees are the neighbor's and while it wouldn't be a bone of contention, it still doesn't feel wise to me -- especially since I am literally the new "kid" on the block. Green Grin! ) There are other things likely to happen with some or all of those trees that will be outside my control, this part I know for sure.
I certainly know that feeling ...
>>>It can climb on that chain link fence as much as its rosy heart desires.
I think that is a better use for a climber. If you have to cut it back to move it, you may not see any bloom next year. Once bloomers bloom on old wood. So the new growth they have put out this year, is the wood that would have blooms next year. The time to prune them is after they have bloomed. Actually, for a climber that's OK because they generally put their energy into growing a large root mass first because they "know" they are going to be big plants. It might be best to move the plant after it has finished blooming. You can have the hole prepared in advance so that it is not such a chore.
>>>I fancy the rose wants to be moved, the way its new growth leans toward the destination. "Take me there!" it says.
Yes and no ...
Climbers are genetically programmed to reach for the light. Species roses are forest edge plants. Many start in very shaded spots, but they survive by "reaching for the light". Most climbers have those genes working for them. Sounds like you are a good observer and will find the right spot for the rose.
Smiles,
Lyn