It is not required for either of these countries to destroy the older ammo stocks.
The question is not destroying old stocks but having to make new stocks incase of war.
I am a big fan of reduced power cartridges for shoulder weapons.
Americans were designing the Garand rifle and Johnson LMG. These two with a less powerful cartridge means that the new rifle can be 2-3 lbs lighter than the historical type, while the Johnson LMG will be less of a beast towards the user's shoulder. Make the new BARs and M1919s for the L-P cartridge.
British were buying the future Bren gun. So no change for them, apart that the Bren can be lighter, or it can longer sustain the firing before the barrel needs to be changed. Same for the Vickers GO.
Germans were designing the MG 34. Again, can be lighter this time 'round.
Actual weight reductions are going to be a lot less than 20-30%. You are stuck with 1920/30 metallurgy/technology.
For example the Pederson rifle weighed 4.1kg, the Garand weighed around 4.7 kg. Some were as light as 4.3 some over 5kg.
No aluminum receivers and few, if any, sheet metal receivers on service rifles. Some of the weight can be blamed on the wood stocks. Unless you reduce the size (length) of the stocks significantly you are stuck with the weight of the wood. Armies had had several centuries to figure out what wood to use in stocks to keep breakage to a minimum.
Now the problem in 1930s for the US was that they were NOT going to go to a low powered cartridge for the 1917 and 1919 machine guns.
The tripod mounted machineguns
were the long range firepower of the battalion. Unless you come up with new weapons (and man power) and/or better signaling for artillery support.
In fact the 1919A4 (the common version in WW II) was not adopted until 1936 with low scale production for the first few years. The 1919 had been designed for tank use and the 1922 version (the A2) used a short light barrel for cavalry use (carried on horse back) but the short light barrels hurt reliability.
The move to lighter weight guns post WW II coincided with much greater numbers of radios allowing for much better artillery support. More motor vehicles (in armies aside from the US and UK) carrying more ammo. In the west the US 105mm howitzer became the De facto NATO light artillery gun. Infantry units could be biased more to short range firepower with much more assurance that long range/heavy support was available in a timely fashion.
The US had adopted the French Brandt 81mm mortar in the early 30s but production may have been slow. Doctrine may have been slow in coming. It didn't help that the US adopted both light and heavy bombs and the heavy bomb only ranged to 1275yds(?) in the initial version, leaving just the light bomb (3.2kg) and machinegun fire for long range (1200-2400yd) use.
In the summer of 1941 with zero combat experience the US army was planning on carrying in a Regiment the following ammo.
8250 rounds per 1917 machine gun
6000 rounds per 1919 machine gun
2800 rounds per .50 machine gun (listed as anti-tank machine gun)
300 rounds of 37mm ammo per gun (90%AP; 10% HE)
300 rounds of 81mm per tube (70%HE light, 10% HE heavy, 20% smoke)
220 rounds of 60mm per tube (100%HE)
28 rounds of .45 pistol.
1720-1748 rounds for each BAR
328 rounds for each M1 rifle
220 rounds for each 1903
These are the ammo totals for the individual armed with the weapon/s or on the prime mover or ammo truck + in the unit ammunition train + ammo train of higher unit.
The .30 cal Brownings are listed has having an effective range of 3000 yds with the 1906/M2 ammo and 4000yds with the M1 ammo (boat tail ball 172-174 grains)
The shoulder rifles and the BAR are all listed as having 600yd effective range regardless of the ammo. Yes their ammo was over powered.
WW II experience would show that the long range machine gun had already had it's day, but radio usage was rapidly increasing from late 1942 onward.
But trying to back date this to late 20s or early 30s calls for changes in doctrine and tactics and communications and logistics.
The US didn't get the first 105 howitzers until 1940, Infantry divisions had 75mm field guns.
Other nations can trace similar histories. British issued tripods to company HQ to be issued for defensive use or for firing at long range for the Bren guns. They probably got lost after weeks/months of movement. Brens had quick change barrels. Issue 3rd barrel for sustained fire rather than hurt long range fire.
MG-34, again an optional tripod mount for long range fire and quick change barrel
Quite a bit of kit for long range fire. All or most kept for the MG 42. and the concept was retained for the MG 3 in the 1950s and later.
The reduced power cartridge is a good idea, but it pretty much forces the adoption of a two cartridge solution.
Now wither that solution is executed within the squad or at higher level (company?) is a good question.
British riflemen sometimes acted as ammo carriers for the Bren gun, refilling Bren magazines for the gunner/s with their rifle ammo.
Other nations did the same thing. Japanese planned one of their guns to use a hopper using rifle clips. Unfortunately the gun did not like full power ammo and wound up needing it's own cartridge supply.