Info of value: SAAMI dimensional standards
Chamber neck diameter: 0.3789 +0.002
Cartridge neck diameter: 0.378 -0.008
Bullet Diameter: 0.357 -0.003
0.9 thou isnt much clearance, but enough. But a minimum spec 0.3789 chamber with 0.0378 case neck around a 0.357 bullet with 2 thou neck tension... 0.378-0.357+0.002 = 0.023, divide by two, thats 11.5 thou case neck thickness. If you buy brass with 12.5-13.5 thou wall thickness, you have to either ream/turn necks or size bullets.
Alternatively, a maximum spec chamber at 0.3809 less 0.0009 clearance, 0.380 cartridge neck, less .357 bullet plus 0.002 tension gives 12.5 thou case neck thickness. Still thin.
Sizing to the 180 HotCor to .356 would certainly chamber - only pulling it down to .357 should fit, but .356 absolutely should unless the barrel chamber is out of spec.