You might be kidding yourself, if you believe fatter tyres give more grip. What they really do is handle heat better on very high performance bikes. With a Commando, you only have 60 BHP to put on the ground. Skinny tyres make the bike more nimble. The friction component is affected by the tyre compound, the weight of the bike and the area through which the weight is applied, as well as the heat in the tyre. A fatter tyre puts the same weight through a larger area, so there is no net gain in friction. A skinny tyre comes up to temperature quicker.
I was reading an article about the Mead and Tompkinson BSA B50 endurance racers. They got faster lap times when they went from 18 inch to 19 inch wheels. The reason probably has to do with the way the bike steers. Larger front wheels increase the trail and can improve the way you can put the power on when coming out of corners.
I use a fat tyre on the back of my Seeley 850, mainly because it wheel-spins when coming out of some corners - which makes the tyre get hotter. If it gets too hot, it would lose more grip. Because the tyre is fat, the heat is handled better. With a road-going Commando, you would never get there.