If you own a 375 Winchester you probably know that it's difficult to get the ammo and the projectiles.
I have a 375 Winchester Lever top ejection so first version.
Have no experience with the cartridge; as far as finding enough ammo for annual hunting trips for those who aren't reloaders, I do see it advertised and sometimes on the WalMart shelf.
For reloading, I do have somewhat relevant experience helping a good friend get his grandfather's homestead and later truck gun 1903 Winchester 38-55 rolling again. This was a while ago, but if I remember correctly, the easiest solution to go hunting with it again was reloading jacketed bullets from Hawke, not one of the other manufacturers.
As far as casting, both the 38-55 and 375 are kind of made for cast bullets - they're cartridges essentially designed for the time when plain old lead bullets were what rifles of that bore and case capacity were fed.
After casting bullets for 40+ years for odd rifles like the Maynard that started me down that path, my one caveat would be that casting may be easy - casting really good bullets that will do everything you reasonably expect of them can have a long learning curve. And it's a learning curve with some "everybody knows" scattered along the way that aren't all that accurate.
If you decide to dive into casting; there's two ways to go. The first is to buy extremely low cost moulds i.e. the Lee mould you mentioned. If you get the results you want out of that off the shelf mould, then you're a winner as many are. If it doesn't provide the performance you want, you're not out much money.
I've tried that a few times over the year with moulds from Lee, Lyman, and RCBS. Some delivered straight out of the box in the rifles I purchased them for - others had me swearing I was going to sell the rifle or the bullet casting equipment.
Ultimately, I got to the point of starting by spending more money on a custom mould, cut to fit the specs of the rifle's ball seat/leade from a custom mould maker. First Veral Smith who lives just a couple of hours away, and now Accurate Moulds, where Tom does phenomenal work.
Anyways, for what it's worth,my position is that success is much more likely and easier to get to with a mould specifically cut to fit your rifle straight out of the mould, with little or no resizing required. The extra cost to have a custom mould cut is insignificant when compared to other costs of shooting those cast bullets.
The debate about shooting as cast versus light sizing is an ongoing one in the Cast Bullet Association world - and that includes among their cast bullet benchrest competitors.
I don't have any beliefs one way or another on that, but I do believe that the extra money spent on a custom mould is quite likely to be money well spent. All the more so when you can get two or more bullet designs cut in the same mould as Accurate will do for a slight extra charge. Trying two different bullet designs for almost the same cost as one. In your case, you could specify the lightest design available for recreational shooting to enjoy shooting with the rifle, and then a WFN thumper in the 200 - 250 grain weights for whatever it is you want to hunt with that rifle.
Fitting cast bullets for best performance involves slugging the chamber to get the dimensions of the ball seat/leade - NOT the groove and bore dimensions as the old "everybody knows" is pitched (usually some version of ".001 to .002 thou over groove diameter"). I haven't joined the CBA in the last few years or gone to their matches, but I didn't know anybody competing in cast bullet benchrest, including for surplus military rifles, that worked with bore/groove dimensions instead of going with ball seat/leade dimensions on their rifles.
If you think about it, when the bullet in the chambered round is a tight fit to the ball seat/lead, when you pull the trigger and that bullet gets a kick in the pants, whatever the groove and bore dimensions are, that bullet WILL fit those dimensions as it obdurates into the ball seat and and moves through the leade into the lands and grooves.
But there are a lot of rifles out there where the ball seate/leade is much, much bigger than anything that the groove diameter is, leading to your bullet starting it's journey to those grooves and lands with burning gases jetting around the sides until the bullet finally obdurates in those lands and grooves to seal against gases jetting around it. That's where leading - and inaccuracy - start.
I would suggest you consider forgetting about traditional lubes, tumble lubes, etc and just move to powder casting your bullets instead. At less than full factory load velocities, powder coating will allow you to skip using a gas check with the protection powder coating gives the bullet.
Powder coating, depending on your technique, will add about .002" to all bullet dimensions once baked on the cast bullet; take that into consideration when choosing bullet moulds and their dimensions after slugging/casting your rifle's bore. With a custom mould like those from Accurate, he will make those dimensions what you specify them to be.
As far as sizing goes, if you aren't going to apply traditional lube while sizing, Lee makes inexpensive sizers. NOE makes some really slick sizing kits (and tempting bullet moulds) that where you can experiment with different sized bullets. Ditto case expanders if you want to neck up cheap 30-30 in stages to use in your .375. NOE is well worth having a look at their webpage and/or making a phone call to ask for their suggestions regarding what you want to achieve.
https://noebulletmolds.com/site/pro...loading/expanders/expander-plug-rifle/page/3/
https://noebulletmolds.com/site/sho.../sizing-tools/sizing_kits/375-caliber-sizers/
https://noebulletmolds.com/site/378-275-fn-brp/
Annealing... I still anneal cases over the flame of an alcohol lamp, rolled between my fingers until too hot to hold. Electronic annealers are the precision (and spendy) way to go. Flaming propane torches with pans of water also work, obviously, but what's also equally obvious is that's far easier to screw up and overheat the cases. There's some easy to do make it yourself kits where propane torch annealing on a rotating wheel is much more controlled. I'm happy to stick with $6 alcohol craft lamp and alcohol being good enough for my needs.
Anyways... there are numerous cast bullet communities on the Web, Cast Boolits probably being the largest, but they are populated by shooters who are obsessed with shooting nothing but cast bullets for everything from antique rifles and calibers to competitive shooters to hunters. Great communities to join, read and learn, and lots of accomplished guys who will be eager to answer any specific questions you might have.
https://castboolits.gunloads.com/sh...r-bullet-suggestions&highlight=375+Winchester
https://castboolits.gunloads.com/sh...4-XTR-375-Winchester&highlight=375+Winchester
You should have a lot of fun with that as you view developing cast loads as a fun project; I really enjoyed getting that 1903 Winchester 38-55 performing again for my friend. Like you, his intentions were that his son will get it - born decades after his grandfather who purchased it new had died.