When I was at Boeing, I spent a full year doing research on unstable approaches. After I left, I published a short paper entitled "The Myth of the Unstable Approach," and you can find that easily enough on line. What got me started was looking at a half dozen ASRS reports of unstable approaches -- all landed just fine. And a half dozen ASRS reports of bad landings all came from, you guessed it, perfectly stable approaches.
The basic thesis was that the term "unstable approach" was a vague, unhelpful generalization that did nothing for accident investigation. Sure, it's good pilot technique, but at the time it was vastly overrated as a safety initiative. In fact, the Flight Safety Foundation finally came around and now talks about go around criteria separate from unstable approaches.
So on to RVs. First disclaimer - approaches are much easier to fly with a constant speed prop than with a fixed pitch prop, and it's easier to fly a precise approach by hand than with an autopilot. Why? With the autopilot handling the pitch, all you can do is chase airspeed.
Here's what I do in my fixed pitch RV-9A at an airport with significant regional jet traffic and Gulfstreams. I fly final on the ILS or LPV at 100 knots so that I can fit in better. At 500 feet, or sometimes lower, I pull the power all the way back and start adding flaps in passing 83 knots. It's not that big a deal!! Maybe it's a big deal in other planes, but it's not in the -9A. Try it both ways in the -6A and see what your plane does. Learn to fly your own plane, not somebody's idealization of how things should be done. And to be honest, I would not have found this technique if another CFII hadn't challenged me to see what my plane would actually do... Besides, if the runway has an instrument approach, it's probably not short. And if it is short, you probably don't need to worry about faster traffic behind.
One thing that I do not have down real well is a go around on autopilot. If I'm slowed down at 200 feet and hit TOGA and full throttle, the plane stays slow and it takes forever for the RPMs and power to build up. (You should not have this problem, I suspect). I may choose to reprogram the autopilot to pitch up to three or four degrees instead of the present five. Part of my solution is that I try not to fly IFR above an overcast that's lower than a thousand so that I have options in case the engine poops out. Following that logic, I'd never fly an approach to lower than 1000 feet. However, weather has been known to change, so regardless of what I anticipate, I need to know how to do a good go around at 200 feet.
When I had my old Cessna 175, 1" of manifold pressure was good for 100 feet per minute change, if I recall correctly, or 5 mph. Go find out what the numbers are for your 6A -- it makes small corrections much easier if you know about how much you need to correct.
So, yes, I agree with your CFII in theory, but not necessarily in practice. Pushing in a few more knobs is not that big a deal if there's good reason to have them set as something other than TOGA settings, like avoiding spark plug fouling. There's nothing time critical when you make the go around decision as the high workload comes later in the missed approach.
So go try things different ways. Find out what your airplane will and won't do, and what fits your personal style. See what you learn. You might get surprised, just like I still do.