Tension will be effectively the same on the rim, regardless of the spoke. A thinner spoke can potentially flex momentarily, but that's a very transient phenomenon (like, milliseconds) as the wheel is rotating.
When you are getting wheel rubbing at the brake blocks, you might also check at the chain stays. This kind of rubbing is more about a hub that can't support the wheel build, or about a slightly looseness in the hub bearings that lets the whole hub wobble just enough, or literally about your frame flexing rather than the wheel flexing. You aren't going to get much of a stronger rim than the ones that come on those wheels. And with that rim design, you have enough latent stiffness that you really aren't going to need a higher spoking unless you are quite heavy (you didn't indicate rider weight). You also didn't indicate which frame.
82kg rider weight but I ride with some grace, not a full on masher! Frame is a Colnago C60.
The rear hub bearings have zero lateral play so I know that isn't the problem but with the narrow(ish) flange spacing maybe it is due to the hub. Your feeling is that rebuilding with heavier gauge spokes won't help much? This chart makes a spoke swap look promising..."The Mavic graph below compares two different spokes to illustrate this – one of 1.8mm diameter, and one of 2.3mm diameter:"
FWIW, I was able to measure my Bontrager/DT rear hub vs the 2015+ Campy Bora rear hub and the Bora's flanges are ~7mm further apart (presumably all on the NDS) compared to the Bontrager. Is this is significant amount in the world of hubs?