The only fly I can see in the ointment here is that if it had ####-on-opening and forward lugs, it would no longer be a Lee action!
You are very right that the Pattern of 1913 rifle was something else. And the ammunition for it also incorporated both the 7mm calibre AND a relatively-large amount of taper. There is an excellent book available on the Milsurps forum (free download) by Peter Labbett and Percy Reid on the design and development of the P.-'13 experimental and service ammunition. It was written before Major Labbett passed away but was never published and it is freely available now to anyone who wants a copy. It is in pdf file form and it is utterly massive when you think that it is for a very short book: just one indication on the tremendously detailed technical drawings it contains.
Again, you are very correct in that there are very few problems with the extraction of the 7.62x39, attributable to a large degree to the large amount of taper and the modest pressure levels, but the same thing also may be said of the .303. I reload my brass until it dies on me and that, of course, always occurs at the range... and I ALWAYS forget to take along one of my (several) ruptured case extractors. But no problem: just jack another round into the chamber, lodge it carefully and slap back on the bolt-handle and they both pop right out.
As to loading one's rifle, I also appreciate the speed and convenience of the charger and use them extensively. With the .303 round, all you do is polish them a little and then load them properly and use them properly and you will never get a failure-to-feed, as the Equipment Report terms it.
Further on the P.-'13, the ammunition was ALMOST rimless: a semi-rimmed cartridge with a lot of taper for easy extraction (and this one needed it) and headspacing on the case rim, which is MUCH easier to control and measure. There were nearly 2 million copies of this rifle built in .303 and they are immensely tough, superbly accurate rifles. Only the over-long bolt throw and the LENGTH of the unlocking stroke keep them from being even better. As well, they are nowhere nearly as convenient to service.
Servicing convenience is not a frill. Think of being in a shell-crater, hurt, nothing to eat for 2 days, you are soaked to the skin in mud and you are cold. You're stuck out in No Man's Land and if you stick your head up, the Maxims start hammering. And there is a problem with your rifle. You have all the tools you will ever need and they are only 3 miles away, but those 3 miles are in the wrong direction as far as you are concerned because the FIRST of those miles is under enemy fire. What do you do? THIS is where convenience of service really comes into its own. You can strip the bolt out of a Smellie and clean the mud out of it with a live round, your finger and a piece off your shirt, but can you do that with a P.-'14? How about remove a ruptured casing? Normally easy with the SMLE, harder with the (forward-locking) P.-'14 and darned near impossible (without tools) with the near-identical (rimless-ammo) M-1917. "In war, that which works best is that which is simplest," said the German General, "What I see here is not simple." He was speaking of the Schlieffen Plan, but he might as well have been speaking of the rifles as well.
After the Great War became history, Remington used up some of the remaining M-1917 parts in building the first of the rare and celebrated Model 30S rifles. A couple of years later, they modified the design slightly, making it a ####-on-opening type and terming it the Model 30 Express. I have had the rare privilege of shooting a Model 30 Express and an M-1917 modified exactly like the original Model 30S, and doing it the same day, on the same range, with nearly-identical telescopic sights. The ####-on-opening feature, I would say, slows the cycling rate of the rifle by about 20%. The longer bolt-throw of either rifle slows it down at least another 20%. This means that if an SMLE can slam out 25 rounds toward the enemy, the M-1917 MIGHT be able to put out 20 (although I am giving it the benefit of the doubt here) and I do doubt that the Model 30 Express would be able to top 15. In a life-or-death situation, a difference in attainable rate of fire such as this can make a huge difference.
As to extraction under extremely adverse conditions, the heat of the tropical countries was the REASON for all those huge old British rimmed 'elephant' cartridges in the first place. If you check the specifications carefully, you will realise that NONE of them even more than approached 40,000 psi and that by far the majority were under 35,000 pounds, PRECISELY to facilitate extraction in a situation in which you were hunting man-killing game and your ammunition had had all day to get to 130 degrees F in the chamber of your rifle. You KNEW you were going to have pressure problems and you REALLY wanted that action to extract properly! And thinking on this even further, you will appreciate the double rifle. They were not made just because those dumb Brits didn't know how to build anything else; they were made for the most dangerous duty in the world, in peacetime. Remember, when you have a failure on one side of a double rifle, you still have the other side: in effect, a whole spare rifle! And the easiest, most efficient extraction with a double rifle demands a rimmed case... so that is what they used. TRY having an ejector failure and digging a stuck rimless cartridge out of a chamber! With the rimmed cases, there should be enough space around the rim to get in a knife-blade to pry the miserable little b*st*rd out.
As to your Brazilian Mauser, friend, you are obtaining what a lot of folks would call the 'creme de la creme': a wonderful rifle, carefully made in peacetime conditions and in one of the world's truly GREAT chamberings. I have used the 1935, although I have more experience with the 1908. Both are most exceptionally accurate and they are light-recoiling and smooth as butter.
And here is something to think on (I know I am certainly thinking about it... and hoarding my nickels, too): REMINGTON turned out a SECOND Lee rifle, the Model 1899. It was chambered for several different cartridges, including the 7x57!
Enjoy your toy!
It's a keeper for sure and you will treasure it for many years to come.