If the main crux is "I don't want to lose control of my character", making it snappy won't really make them appealing to those players even if it's beneficial to have more responsive Rescue function.

An alternative that I could think of is to just rip off OC Phantom Oracle's targeted Invuln button, but make them last only 2-3 seconds probably. But that might open up another issue that I cannot think of for the moment.