[If my house was on fire, there are more important things to grab than a detector, but I get your point. I would grab the only one I have right now which is the Quattro. The others are gone as it's questionable whether I can continue to detect, or not, because of serious back issues. After 45 years in this hobby, it's hard to walk away, even if I can't hardly walk.
As far as quicker resetting goes, I would guess the fastest would be the E-trac. However, it also depends on how you run your machine, sensitivity wise, and your sweep speed as well as environmental conditions (soil moisture, mineralization, EMI, etc.).
One other thing I'll mention is the quality of the signal and tones. I found the E-trac didn't give me the same "silver" tones that the Safari does. Maybe it's just me, but I didn't like the E-trac. I don't like to "fiddle" with settings or programs, etc., so that's why I'm drawn more to a simpler instrument without all of those various "features". I've been fortunate in that I can afford to buy any unit I want, so that hasn't been a limiting factor on which machine I prefer. I've used Minelab detectors since 1996 and still feel they produce some of, if not, the best instruments available. After using multi-frequency detectors for over 20 years, I just can't get along with a single frequency model anymore.
Ok, off the soapbox...