In the 1960s, the NRA did a lot of technical work on cast bullets, what worked and did not, and why. Some of those works were compiled and are now available on-line. I will try to find links at Cast Boolits and LASC. You ask a lot of questions, and I will try to answer them based on my recollection of the NRA articles and my experience. You have a .300 Win Mag, and you have used the "Lee Liquid Alox" (aka "LLA") dip or swish method of bullet lubrication. LLA is a product of the former Alox corporation, now owned by Lubrizol, and is Lubrizol Corporation's Alox 606-55. Lee buys it in quantity and repackages it in tiny bottles, which costs a lot.
Alox 606 is a solid. Melts at 245 degrees centigrade. It is diluted with 45% mineral spirits to make 606-55. There is at least one other vendor who offers the same as LLA, and other mixes based on it.
You now have a Lubricator/Sizer, which will use a grease-like lubricant such as 50% Alox 2138F/50% Beeswax, a formula recommended by those 1960s reports by NRA, so called by many "NRA formula", but also called by the name of many suppliers who bought 2138F and beeswax and sold it. Lubrizol stopped making 2138F some years ago, and offered a replacement of Alox 350 which differed in that it lacked a small portion of microcrystalline wax. About 2 years ago Lubrizol announced that it was stopping making Alox 350. I have heard nothing regarding what suppliers are using instead of 350. Alox 2138F and 350 were classified as calcium soaps. The NRA formula is particularly smoky at low pressures.
There are many other grease-type lubes, suitable for use through a lubricator/sizer. Various greases such as Lithium grease mixed with beeswax is one, a synthetic 2-cylce oil mixed with beeswax is another. You can read about this stuff forever.
The compilations of the NRA technical reports go into a lot of depth about what types of barrels generally work better with what barrel configurations. Groove diameter, throat configuration, rifling twist, and pressure are just a few considerations. There are lots of families of bullet designs, some generally working with some configurations. Rifle bullets I have used a lot include "Lovern" (lots of grooves) and "Bore Rider".(long smooth nose of land diameter, followed by several driving bands of a little over groove diameter). A common feature of rifle bullets intended to go over about 1200 fps is a base support called a "gas check". In general, the biggest diameter of the bullet is a little larger than barrel groove diameter: I do this for the bullet to fit the throat ahead of the chamber, engraving a little bit into the rifling, which supports the bullet on firing, preventing it from slumping to the side, which always produces bad accuracy.
Extending the cast bullet back into the cartridge case is generally avoided, but it can work. The NRA technical studies had pictures of a lot of things to be avoided, including bullets which had slumped to the side on firing and always produced poor accuracy, and long cast bullets which had their base seated well below the neck. The deep seated bullets they had recovered after firing, and the effect on the deep exposed Lead was ugly. They also worried about a gas check being left behind somehow in the case or in the barrel.
Cast Lead is not as strong as a Jacketed bullet. You can not use full Jacketed data loads, or the bullets will fly wild and maybe break up. Even if you harden it with Tin and either Antimony or Arsenic, then drop from the mold into water, they won't take it. You won't be able to use reduced loads of the slow powders that you would use in the .300 Win Mag, or you will encounter Secondary Explosion Effect. Stay away from reduced loads in big cases using slow powders, unless the powder manufacturers have recommended a load. You also have worries in such big cases with getting a double charge of powder, which would be hard to see given the case size, and would also blow up a rifle.
http://www.nzha.co.nz/wp-content/uploads/2015/08/CastBullets-s.pdf
http://www.nzha.co.nz/wp-content/uploads/2015/08/NRA-Cast-Sup1.pdf
https://castboolits.gunloads.com
https://forum.castbulletassoc.org