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How do you accomplish this with a "controlled round feed" Mauser 98 type action?
If it is a commercial rifle that is sold as a "controlled round feed", it will have a User Manual that will tell you how to load it. Like Ruger 77, some Win 70, etc. - they do not have some details that an original Mauser 98 had, but they do have the large external claw extractor. A 375 H&H was not a "standard" factory Mauser product, I don't think - but many were made up (milling, machining, metal work required) from original M98 receivers. Not going to single load an unaltered Mauser 98 - although some have been modified to do so, but are not "original" design. Some rifles have a fixed floor plate, so usually not easy to open it to load rifle. If claw nose has been altered or worn a bit, is often possible to use left hand and squeeze the claw extractor (behind the bolt collar) towards the bolt body - this lifts the claw slightly away from the bolt nose, (or at least reduces the sideways tension that is on it) and sometimes will allow that claw to ease over a cartridge rim, as you close the bolt with your right hand. I have a Husqvarna 649 in 9.3x62 that requires me to do so, if I really want to have six on board, instead of the "normal" 5 rounds. So, makes a difference if you have a genuine Mauser 98 or a Mauser 98 "type" action - sales people have been involved in that word play for years.
I know a couple US people who insist on referring to their M1917 Enfield rifle as a "Mauser" - it is not. Read up on the US Army documents from WWI - that rifle IS made to be single loaded - the claw nose is significantly larger and different shape - the earlier P14 often used for belted magnum conversions - same story - the claw is not the same, at all, compared to any mauser. Hence some confusion as to whether a "Mauser" can be single loaded or not - goes to properly, and specifically, identifying the action. I have a M1917 here that was altered into a 300 Weatherby - which is same belt and length as your 375 H&H - load magazine normally, press last one down to allow bolt to get on top of it, and single load the last round into the chamber. But is NOT a "Mauser 98", but some might call it a Mauser "type" action, and it is most definitely a "controlled round feed" action.
Probably worst that can happen by trying to force it, is to break off that extractor's nose claw. Now have a push feed, with magazine full, with no extraction function, so basically a "single shot" to fire and jack knife to extract case, and nothing but double feeds and jams?