From Wikipedia
".38/200 was the British service cartridge adopted in 1922 for .38 calibre pistols and revolvers which replaced the larger .455 and .476 inch handguns.
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Webley demonstrated a lighter version of their Mk III revolver with modified .38 S&W ammunition with a heavy 200 grain bullet. It received favourable reports from the Army and the revolver was accepted in principle assuming an effective round was provided for it.
As Webley had used .38 S&W for their revolver, and the cartridge length was fixed by the size of the cylinder of the revolver (the same as for the wider .455), Kynoch produced a cartridge with the same dimensions as the S&W but with 2.8 grains (0.18 g) of "Neonite" nitro-cellulose powder and a 200 grain (13.0 g) bullet. This combination gave a velocity of over 570 feet (170 m) per second at 50 yards, although the bullet become unstable after penetrating the target. This was deemed satisfactory and the design for the .38/200 cartridge was accepted into Commonwealth Service as "Cartridge, Pistol, .380" Mk IIz", firing a 180 gr (11.7 g) full metal jacket round—after it was realised that the 200 gr lead round would contravene the Hague Convention, which outlawed the use of unjacketed lead bullets in combat.
The cartridge was finally phased out of Commonwealth Service in 1963, when the Browning Hi-Power was finally issued to most units.
The Cartridge, Pistol, .380" Mk IIz is still produced by the Ordnance Factory Board in India, for use in revolvers of the Indian Army and many African countries.
Revolvers chambered for .38/200 will also fire .38 S&W (AKA .38/145), .38 Police Positive, and .38 Banker's Special cartridges, along with the .380" Mk IIz round."
A quick check of my very old Lyman manual didn't show any 200gr loads, by a cross check with 200gr 38 Special loads using Lyman's 358430 round nose seems to indicate that 38 Special starting loads might be near your max in a 38 S&W. A chronograph to work to the issue velocity would be helpful.