375 can be built on 98 Mauser. Duane Wiebe does it all the time and you can order his informative how-to booklet from him for $25. It would be very helpful for your gunsmith. The advantage to building on Mauser 98 is the actions are plentiful and can be picked up reasonably. Standard action 98 has shorter pull stroke and lighter weight than magnum Mauser actions (which are hard to find and very expensive). Another important advantage is their popularity as a build action means lots of aftermarket parts are available. I built this 404 Jeffery from a postwar Czech Brno cz.24 military surplus 8mm (that had been rebarreled in 30-06). I seem to recall I paid about $260 US for the action. I bought used Model 70 Safari Express iron sights off ebay for $150 (a bit pricey but essentially new condition), new 3-position Model 70 safety from eBay at $200, new Timney trigger from eBay at $85, hinged floorplate bottom metal ordered from Swift Blackburn for $400 (at least two other vendors also making them), new one-piece scope base ordered online @ $65 (replaced later with a lower one in discontinued model @ $10!), barrel from Lija at $400, mounting the barrel = $600 (threading, reaming, and head space), new Warne Quick detach scope rings online for $65 (a good buy!), semi finished stock from private individual ad on Gunpost at about $110 US. I put the gun together after making modifications to receiver (feeding rail, extractor, and loading ramp) which requires a good gunsmith (maybe $400?). A fella in New Brunswick did the bluing for $150 Canadian after I did the prep work. A local machinist opened the bolt face using Weibe's booklet for guidance (he didn't know what to charge so I gave him $100C). This is the completed project (April to August 2023). I have posted a video of me cycling the rifle and it is slick, fast, and faultless.
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Last month while looking for more ammo components I spotted a nice used stock at a very good price. What the heck, I needed something to do. Required more work than expected (including fitting crossbolts and wrist reinforcement rod - both of which I've never done before) but it turned out well. Also added a new 1-4x scope ($130US).
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So that will give you a rough idea of expenditure. If I'd chosen another action to build on, the aftermarket options probably would have been more limited and more expensive. Your gunsmith might want to modify the existing bottom metal but I'd advise spending the money and ordering one. 375 is a good choice because stuff for them is easy to get, especially ammo and components (404 not so much!). Definitely spend the money for 3-position Model 70 safety. For comparison, those safeties can also be had for building on 1903 Springfield and 1917 Enfield but at upwards of $500. Bottom metal for them is much harder to find (I can't find anyone making Springfield bottom metal).