Wow… that’s no good (you mean the spider actually made a break for it in your house somewhere?). I guess you’re talking about slings then (as I know they can get a bit of speed up).
Anyways are you moving the T to an enclosure the same size? If the old one is smaller maybe try putting the old one inside the new one and sort of “tip” the T in that way using pencil or something being very careful not to make the drop too big or that anything from inside the old enclosure falls on it etc?
Only other thin I can think of is actually letting the T “escape” the old enclosure inside a larger plastic container or something and moving it that way? Just a thought (I’ve always been able to move mine by either container or in certain cases by hand).
Other than that I am still trying to think. I’ll have a look in a few books now and see if they have any ingenious ideas.