Can I transplant my Toona sinensis tree?

I have a Toona sinensis tree in my fruit jungle. I've been given a new apple tree (the Bardsay apple Yay!) and I'm thinking that where I have my toon tree planted will be better suited to the apple. It is fairly sheltered, with moderately deep damp soil (and I have adjacent apple which are starting to fruit well), but I think it is too damp and cool for my Toon.

My Chinese Toon tree in the fruit garden

What I'd like to do is transplant the Toona to my 'secret garden', which I have been doing some work on this year and is better drained and a bit sunnier (although probably a bit more exposed to the East). The Toon is growing slowly where it is, is probably about 4 feet tall now after three years, but is not really thriving - it is danger of being swamped by my raspberries, and I think it may prefer the company of Hosta and Udo instead....Has anyone experience of transplanting their tree?
If I do transplant it, I understand that they coppice well, but can you root the top bit that is cut off? I'd quite like to have another tree, since they seem a bit slow growing here. Otherwise I'll never feel that I can take a leaf to eat, which is sort of the point - although the foliage is quite pretty.

Hi Nancy. I don't know how easy cuttings are to strike from this tree, but we have one that the former owners planted in the forest garden and it sends up root suckers like there's no tomorrow. Have a look around the base of the tree (ideally before the leaves drop off) and see if there are any shoots. With a sharp spade, you can lift those over the winter and either pot them up or plant them out in their new locations. That will give you some backups in case the main tree doesn't take kindly to being shifted.

Is your tree one of the ones with edible foliage? I know that technically toon leaves can be eaten, but ours are beyond vile. They smell like a mix of old socks and onions gone bad, and the flavour is about what you'd expect from that olfactory impression. For this reason, I'm not attached to the tree and its suckering habit is making me look longingly at the chainsaw.

Thank you Phil for the advice - I'll have a look for suckers (when the weather gets better). I've only had a nibble on an odd leaf so far. It came from the Agroforestry Research Trust (I think), so I'm hopeful it is one of the more palatable varieties!

Given the size of your tree, I suspect that as long as you get a decent amount of the root ball when you lift it, all will go well.