Your card is in some jeopardy
I have two Sako .375 H&H rifles, a L691 Hunter with a 24" barrel and a M995 carbine with a 19.5" barrel, and I have to say that the stock geometry makes a big difference in felt recoil. The M995 is more pleasant to shoot despite being quite a bit lighter.
For practice loads I'd recommend starting with minimum (or slightly reduced) H4895 loads combined with 235 gr or 250 gr bullets and working up from there if needed.
For range practice I'd recommend getting a PAST recoil shield - I always use one when shooting off the bench.
View attachment 1130153
Which Sako model do you have?