New barrel

I am anxiously waiting on the delivery of a 375JDJ custom ssk barrel with full rib and porting. I have a 375 already but wanted a custom with a full rib. I thought about the 309 but didn't want to bother with fire forming cases. I ordered the bushnell elite 2x6 scope and rings also. I guess I have the addiction because I know have two 375 barrels and two 45-70 barrels for my contender.
What is a softer bullet to shoot than the hornady 220 grain soft point. I have tried accubond and Sierra but they didn't mushroom.

Hawk bullets are perfect for deer. I wouldn't count/depend on them for larger game though. They will expand!

To my knowledge there is not a standard factory bullet "softer" than the Hornady 220. If you could not get the other bullets you mentioned to expand it's probably due to too low velocity. You didn't state your velocities, do you have a chronograph or access to one? Also you didn't state the distance at which you checked for expansion. Personally, I've never had any problem with expansion with any bullet I've used in the 375 JDJ.