Even if the case seats, there may not be enough neck relief to allow the bullet to exit the case without generating excessive pressures.

Maybe you could make up a "blank" round with NO BULLET {but enough pressure to obturate the case} with a Lott case, fire it and then take a bullet and push it in the extracted but unsized case. If it hangs up or is very tight, not enough neck relief.

Somebody who can study the chamber drawings can help more.

Bonanza, you already have a Lott case.

Take one of your .375's and trim to Lott length and go from there. Any blank that obturates the neck fully will take care of the body, too.