Hi,
It could work, but remember that you wont have much of a shoulder for headspace.
You will also need a custom barrel with a tight twist for stabilising heavy bullets, more likely cut rifled then ,unless you find a barrel maker who has the buttons for such tight twist.
You are going to need to have a reamer made and a set of dies as well.
It can be done, if you have the money
ssk is already producing a 375 whisper, that might be an easier way to go.
Good luck
ND