dont understand whats wrong with the 375 NE 2 1/2"
if you have 303 brass just make your 375 NE brass out of this

open 303 brass

10mm brass tube
pressed in 303 brass
anealed
cut to right lenght
polished and resized
375 NE Bertram brass

pressing the tube into the brass

drilling the tube inside with a 9,5mm drill

side by side with bertram brass