I have built Many single shot rifles on falling block rifles designed for magnum cartridges and other falling block actions designed for standard cartridges. there are several falling block actions that come to mind for you interest in the 300 or 375 H&H. The browning 1885 and the Ruger #1 that are available. Three of them were on the low wall browning/Winchester. One of my favorite rifles is A 22 K Hornet on an original 1883 low wall. And some of the magnums were a 7 RM, 7 STW, 300 win mag, 300 STW, 375 RUM, 404 Jeffery, 416 Rigby, 425 Express, 458 Win mag for a range of cartridges
And they are all very good shooters and have not given any problems.
They are however difficult and time consuming to build as Shortgrass said but extremely fun to shoot. I have also built 45/70, 45/110 and 45/120 black powder cartridge rifles on these actions
and can vouch for their strength if you want to go this way.
I have always had a love for the falling block action and just went with actions designed to do the job. I have never built one on an aftermarket action so I would not be of any help on their strength.
J E CUSTOM