Another person was asking a similar question a few posts down. The first area to consider is that you have a reg. case bolt face. Any of the magnum cases will require surgery to be done on that bolt face (may not be a big deal).
Weatherby's are very strong action but due to their multi lug bolt, most don't use them for very accurate work. Good chance of less then ideal lug/receiver engagement.
I too would recommend selling the rig as is. Take the money and buy a commercial action (Rem 700, Savage 110, or Win 70) in a magnum calibre. If you wish to go custom, there are many excellent choices and money spent there can have positive results.
Invest in the best barrel and install you can. The chamber and throat dimension are very important. The gunsmith of choice should have some BR or High power experience under his belt. This will have the largest bearing on accuracy in your rifle.
Tune that trigger to something light and crisp (personal preference here). Put the whole rig in a suitable stock and mount the best optics you can afford.
You indicate that budget is not that big a deal, so you have fun building your Ferrari. If the costs get a little out of hand, I would suggest one of the commercial actions mentioned, and put the extra money into the scope, barrel, and practise.
Remember that for the first thousand rounds or so, a well built rifle on a commercial action has better mechanical accuracy then a new shooter can shoot at long range. Some of us never get better then our equipment.
Have fun building your dream rig...
Jerry