I am n0t a gunsmith but my first question would be whether the action rails were modified when the rifle was rebarrelled? The .375 H&H and .375 Weatherby have exactly the same headsize (the .375 Weatherby is basically an improved .375 H&H) so one would expect the rear of the case to be retained without problems.
However, it is possible, as your gunsmith suggested, that the Weatherby case is not stacking properly because the shoulder of the case is fatter and this is causing the rounds to project out from the action side rails and this allows them to stick up at the rear. The solution would be to have the feed rails reworked to suit the .375 Weatherby. What I have found is that many Mauser 98 owners (and this includes many gunsmiths, too) don't fully appreciate the importance of the size of the magazine box and the shape of the feed rails when rebarrelling for cartridges of a different size or shape to the original round. Having played with a lot of Mauser 98 projects, I have learnt the hard way about the importance of magazine box size and feed rail shape - I still do not understand it fully, but know that it is something that is vital to any rebarrelling project.
To illustrate this point, if you can get hold of a copy of the book "Original Oberndorf Sporting Rifles" by Jon Speed, Walter Schmid and Reiner Herrmann, and go to page 127, you will see that the Mauser factory had different magazine box sizes for each cartridge that they made. While the same dimensions can be used for cartridges that are very similar in size and shape, when you change the shape substantially, such as blowing out the front of the .375 H&H to make a .375 Weatherby, then the dimensions become marginal and changes need to be made - in this case the magazine box is probably ok, but the feed rails will not be ok.
If you decide to get the feed rails re-worked, make sure you get someone who knows what they are doing, or you will never get reliable feeding.
The other option, and in my opinion the better option, is to rebarrel back to .375 H&H. What isn't generally appreciated is that the .375 H&H is more than adequate for most hunting purposes and if you need more gun than a .375 H&H, then you need to look at a .416. 404 or .458. Also, if you read some of the gunsmithing publications in relation to Mauser 98s, you will find that the standard length Mauser 98 and some of the newer Manufacture M98 clones, such as the Zastava M70 magnum (and the Remington 798 is based on the Zastava action) are still only standard length actions and are not suitable for cartridges that operate at greater pressures than factory .375 H&H rounds.
If you really have to have a .375 Weatherby, then you really need a true magnum length action such as a CZ 550 Magnum.