Now THAT is some good advice!
I guess if I read more books on the subject, it wouldn't be such a revelation to me...

Back to the OP, I agree that good modern barrel steel does, in fact, mitigate the concern of using higher pressure cartridges than the original chamberings produced.
My understanding is that, with a clean greaseless case and chamber, the case adheres to the chamber walls at 10Kpsi.
I suppose at that point, the type of powder and the pressure curve produced by the specific load would have some bearing on how much breech thrust occurs before the adherence point is reached.
I also think that the cylindrical (more or less) form of the 375 and 405 cases helps in this regard.

All that said, your rifle is a classic, even if modernized with the new barrels so to speak.
There is no end of enjoyment shooting such a rifle at reduced loadings, more or less as it was built for.
If the 405 nitro loads are not to your preference, you could rechamber that barrel to 450/400 3-1/4" and load it to NfB pressures which would be more in keeping with the rifle's era.

Also, it would be great to have a competent smith make the rifle into a legitimate switch barrel.
That would be cool!