A heavier bullet causes longer barrel time, so the pressure has more time to peak when the bullet isn't too far down the bore. A bullet that is too light for the powder burn rate can lead to a lot of velocity spread in very short barrels. We had a fellow with a 1 7/8 inch snubby in .38 Special getting velocity variation from about 490 fps to 650 fps from his load on another forum (I forget if the bullet was 125 grains or 110 grains). Going to a faster powder, the velocity spread came down, but 600 fps was as fast as he could safely go with the faster powder.
It is a factor that muzzle energy will tend to peak with a bullet the right weight and seating depth in the .357 Magnum. In a full power .357 load for 3" and longer barrels, 125 grains is usually the sweet spot with H110/296 and other magnum-specific powders, but the short barrels keep those powders from being utilized to best effect with that bullet weight. .38 Special has the same issue with short barrels. I noticed, as Hammerhead must have, that Speer Gold Dot .38 Special and .357 Magnum Short Barrel Ammunition uses their
135 grain bullets. That's weight is probably a best compromise value for the snubbies in these cartridges. Also, the Gold Dot is a plated jacket bullet that is harder than lead but softer than standard jackets, and that probably ensures its expansion at lower velocities than Jackets will work well with. If I were doing your project, despite Hammerhead's disappointment with the bullet's length consistency, I would likely piggy back onto Speer's experience with snubby loads and use this bullet as a starting point anyway. Nosler used to make a 135, but I don't see it listed on their site.
For a 2 inch barrel, QuickLOAD thinks a number of powders could still achieve pretty good velocities at that bullet weight and despite the short barrel, though I don't fully trust it's predictions with such short barrels, so I won't mention numbers here. But relative comparisons are still promising. It predicts 2400 will be a top velocity producer in this barrel length. Blue Dot is another possibility, but after Alliant's warnings against its use with 125 grain bullets and the fact 2400 got slightly more velocity with slightly lower charge weight in the short barrel, I figured, why mess with it? Unique does well for a tamer load. Power Pistol is known for fireball brightness, but at Alliant's listed load is an in between velocity producer. Per Hammerhead's point, 2400, Power Pistol, and Unique all have recipe's for the 135 grain Gold Dot, specifically, at Alliant's web site, which is another reason to work with these powders if you are going to try that bullet. Just remember Alliant's "recipe's" are max loads and their manual says to knock them down 10% to start. I haven't loaded with 2400 recently, but my recollection is that it has a yellower flame than the sphericals produce, so the fireball is less blinding. You will have to experiment to see which works best for you, though.
One last point: For the short barrel consistent ignition is extra important. Because a snubby is light, bullets are more subject to inertial pulling under recoil, which makes a bullet stick out of the cylinder and jam rotation. For both of these reasons, a really strong crimp is extra important. I can recommend the
Redding Profile Crimp Dies, specifically. It's roll crimps can be made firmer than others without bowing the case out below the crimp. Lee now makes a
Collet Style Crimp Die for 357 Magnum that is less than half the cost of the Redding product and that might provide an even stronger crimp, but I just got one and haven't yet tried it out, so I haven't proved this to myself one way or the other.