If you buy witchmail on ivy, it will just constantly refresh your ultimate ability that goes on cooldown for 5 seconds when you get damaged, I don't believe calico and ava works like this. Though I suggest making the cooldown time of cooldowns from taking damage not interact with witchmail...
There are multiple abilities such as Pocket teleport, Yamato Grapple, etc, that can get you out of the spawn. In addition to multiple items that can get you out such as Phantom Strike.
On top of that, Silencing, Cursing, counter spelling, can all prevent a doorman from pushing you into the...