An hour and a half later, after initially viewing your post, (found via weetreebonsia's resteem), I think you should not worry about propagating your tree.
I found this link:
(http://forums2.gardenweb.com/discussions/1657116/advice-on-royal-empress-tree).
10, thats TEN years worth of comments about those trees,(2007-2017).
I do so like waking up and finding something interesting to occupy those first few hours of the day.
I am not sure what side of the fence I stand on when it comes to invasive plants, both sides I guess. In a city or urban environment, I do not think there is such a thing as an invasive plant,(just invasive buildings and people). One of the 204 post on the above mentioned link was a picture of a tree, (I am guessing the invasive one), growing right next to an abandoned warehouse. So what was the invasive, the tree?/or the warehouse?. In a country environment, there are, (if you are lucky), the real wild/native lands to be considered.
Thanks to both of you for some interesting searching/research to do.
I am sorry if I was not clear, but these ones are not invasive, as I mentioned in the post. They are a sterile variety - the seeds cannot reproduce.
Check this out: https://www.fast-growing-trees.com/blog/royal-empress-trees-invasive-heres/
But you're right - humans are perhaps more invasive than anything. Still though there is a good point in not introducing a species into an environment where everything else won't know how to respond to it.
We also have Chinese Privet, which is considered invasive - it was growing here when we bought the land - but goats LOVE it. So, in that way, invasive plants can be useful - because we can rotate goats around to different stands of this stuff and they will eat it down and in a month it will grow back up.