Very well put Mike! It's tough to put yourself under the microscope like Flyguytki has done, he's to be commended for that!
Great outcome, nothing bent, nobody hurt. Now everyone can armchair QB the thing and we'll all learn a little bit.
A not-so-quick story: I bought my RV-6 in mid May this year. When I went for a quick check flight with the owner/builder as part of the pre-purchase inspection, we had a little problem... I was just along for the ride more or less, as it was still his airplane, and I had oh, about 15 - 18 hours in a single/piston engine in the month prior in preparation for picking up the RV. I had actually added the ASEL two weeks prior, and completed the RV transition and TW endorsement two days before with Mike Seager. With so little recent single/piston time, I still wasn't 100% comfortable in the single engine (still working on that now), and he was PIC.
On the takeoff roll, with the mains just coming off, the engine stumbled. It only lasted a moment, but to me, it was pretty significant. We were on a 5400' runway - and he continued the takeoff. I advised him that we had plenty of room to stop, and by then we were off and climbing. I said (a couple of times) that we still have PLENTY of room to land - and he continued. He was semi-unresponsive to my input, but I did not attempt to take the flight controls. About the time we had progressed to a point that a safe landing after an engine failure would have been very questionable due to our altitude, position, and the trees surrounding the field; the engine stumbled again. Only for a moment?
I've been flying for many years, I've had my share of emergencies, including an engine failure in a single engine helicopter, and I've flown about 1000 hours in combat. I have never, ever been so uncomfortable in an aircraft before. Quite frankly, it scared me. Mostly that was because I was not in control of what was going on I suppose.
We obviously got the airplane back on the ground OK, did some trouble-shooting and found the problem, found two actually. I had already discussed the flight with him, an informal and gentle de-brief if you will. He was not pleased with himself for continuing the takeoff, and of course he understood that I was not happy about it either! When it came time to fly again I did a fairly comprehensive brief, and we discussed contingencies. He was comfortable with that, attentive and much more prepared when we went back out. That flight went fine.
The point is that we all need to be prepared all the time. He was not mentally prepared to abort, and so he didn't. I should have had a brief with him before the first flight, but I didn't. I know I'm not as on top of it as I could be, but I try to brief myself each departure on what I will do if the poo hits the fan. Inbound to an unfamiliar field I'll try to take a look around and make a departure engine failure plan. I know how high I need to be to consider a turn back to the runway. I make almost every approach the old school way, power off at the abeam point to the landing. I try to never be in the pattern at a position I could not reach the runway from. I want to be prepared, and the fact that flying around on one engine still feels like an emergency procedure helps keep me focused on that.