My low-wind kite this season has been a 10m Flysurfer Soul (which I know isn't what you want, but that's not the point), which I feel like is good down to about 11 knots, and after that it's too light for me to use it reliably. On the other hand, my mid-range kite is a 7m F-One bandit, which I can ride down to about 13 knots, so same as you, the extra 3 meters only buys me about 2 extra knots of wind. With better technique maybe I could get an extra knot or two out of this, but I don't like kiting so close to the edge that any tiny mistake results in a dropped and non-relaunchable kite. I could also maybe get an extra knot of low-end by going to a lighter single strut kite. I'd rather wait for the wind to come up an extra knot or two. I also usually kite in higher-wind locations.
I think that even in smaller kite sizes, you can almost always build enough power to foil, as long as you can keep your kite in the air. I think what helps with this at the very low-end is a very lightweight kite. If it's blowing right around the minimum to keep your kite flying (say 8 knots for some hypothetical kite), a short lull to 7 knots can put your kite in the water if you lose any board speed. A lightweight kite will float in the air with less wind than a heavier kite that's otherwise equivalent.
You get diminishing returns with bigger kites, because the force of the wind is proportional to the square of it's speed, so if you double the kite size, you can "catch" twice as much wind, but if you double the wind speed, the wind has 4x as much power. The converse of this is that if the wind drops by half, you need 4x as much kite for the same power, so at the bottom end of the range, kite sizes have to increase by huge amounts to keep up with small decreases in wind speed.
Anyway, it seems like most people can ride a 9-10m in 10-12 knots if wind and be happy with it, but I think a lot of pushing the limits of the bottom end of the wind range is down to technique, and never letting the apparent wind on the kite get so low that it can't keep flying. If you're good at this, you can probably keep the effective speed a little bit higher than someone who's not as good at it, thus letting you use a bit smaller kite.
Anyway, it sounds like you're a better foiler than me (I'm planning to try and learn tacks this summer), so I'd expect you can get an extra knot or two lower than I can (which is what it sounds like), and a 9-10m might be big enough for you even at the low-end (I wouldn't even bother trying to kite in 6 knots, but I live in a location known for big winds).
Finally though, what does the math say?
If the power of the wind is proportional to it's speed squared, but the power of a kite is proportional to it's area, then you need 20% more power to fly a 10m over a 12 meter, which means you need about 1.1x the wind speed, which means if you can fly a 12 in 7 knots, then you can fly a 10 in 7.7 knots.
This math also suggests that if you can fly a 12 in 7 knots, you can fly a 9 in 8.1 knots, and a 6 in 9.9 knots. This math is too simple to count things like the relative weight of the kite per area at any given speed, though. Aerodynamics is hard.
Anyway, that was a whole lot of text to say "going from a 12 to a 10 probably only costs you about 1 knot of bottom end wind speed".