Thanks for the follow up and for the further explanation.
I have made some quick changes to the SubTree node (attached for you here) and now changing the target SubTree, even while the SubTree node is running -both in editor or in runtime- should work better (no reference lost and no need to stop/restart).
Please note though, that if the change happens while the SubTree node is running, the actual change will take place only once after the previous target SubTree is finished first (return anything other than Running).
Can you please test it out and let me know how it works for you?