I'm probably preaching to the choir by now, but I am in full agreement: Dough from a spiral mixer has some really nice properties. I've too have made dough by hand, and I've used a couple of other mixers (Kenwood with J-hook, Kenwood with spiral-hook, Santos fork mixer). I've always been happy with these tools, no complaints really. But the spiral mixer is really something else. It amazes me how homogenous, tight, soft, airy and ... lovely and enjoyable! ... the dough comes out and ends up.
I seem to return to about 5 minutes mixing time for the softest result, I add everything (except for oil) to the bowl and let my Sunmix run at it's lowest speed for 5 minutes (68 rpm). If I add oil I'll add it at the 3 minutes mark.
The result is a dough that isn't very well developed with "short" gluten chains. That is to say it won't pass any kind of window pane test and tears quite easily if you try to make one. Still after an hours rest it allows making very smooth balls and has a much more developed gluten web.
Once finished proofing and getting opened into skins it's a pleasure to work with.
Your mileage can and will probably wary a lot! 
Edit: Note that this is for normal pizza dough at around 60% hydration. For higher hydration (read 75-80%) I do use the higher speeds and let it go for a longer time. For this kind of dough I'll normally start with around 65% hydration at middle speed (110 rpm) once the pumpkin has taken shape and I see that the gluten is beginning to get well developed I'll up the speed to max (208 rpm) and drizzle in the remaining water, the whole process takes about 10 minutes.
Jack, I have the same mixer (Sunmix6) and have seen you mention "five minutes on slowest speed" a number of times before. I've been wanting to ask you about some details, but your post above answers all my questions.

After purchasing the Sunmix last year, I went through a lot of testing with different speeds, durations and combinations. For what it's worth, I too have now gravitated toward a very simple procedure, which works really well for my usual doughs (~24 hours, ~65% HR, Caputo Pizzeria): Mixing for a total of 7-8 minutes on 125 RPM. At this point the dough is well developed, probably a bit more than yours. The friction factor in this case is close to 7 °C, a fact I use to control the water temperature so I end up with my target FDT.
So predictable!
My only "problem" is that the machine is heavy (I have to carry it up and down a flight of stairs each time I'm using it because of my tiny kitchen size

).