I wish to add my usual warning about old military rifles. Your action was made in the 1890's, at a time when the understanding of steel metallurgy was just beginning and process controls were human eye balls. Sometimes taste and touch, but it is all pre vacuum tube*. While a modern small ring could take more load (pressure times surface area) than an original, originals need to be kept within the pressure limits (load!) of the period. This is all due to the poor quality of period steels, the fact these were plain carbon steels, the overall uncertainty of the end quality of the things, and of course, the unknown severity of previous usage.
Anyway I went out and shot Surplus Swedish ammunition in a M1896 and in a carbine. It was surprising what five inches makes in velocity, the 29" barrel really pushed these bullet much faster at the same pressure.
My loads, a 140 grain Hornady with IMR 4350, while it is a trifle faster than the military loads, I consider them pressure wise, equivalent. This is based on nothing more than comparing velocities and making the assumption, that similar velocities mean similar pressures. Of course this is not true, could be more, could be less, but overall, I think this is a reasonable approach.
M1896 Infantry Rifle 29' barrel Carl Gustafs mfgr 1903
17-Aug-06 T = 85 °F
143 gr FMJ 1986 Swedish Ball
Ave Vel = 2610
Std Dev = 14.38
ES = 45.59
High = 2633
Low = 2587
N = 8
M38 Infantry Carbine 24" barrel
28-Oct-94 T ≈ 60 °F
143 gr 1986 Swedish Ball OAL 3.065" 47.4 grs powder average
Ave Vel = 2427
Std Dev = 22
ES = 62
Low = 2395
High = 2457
N = 10
M700 22" Barrel
143 gr Swedish Ball 1986 headstamp
2 Feb 2008 T = 54 °F
Ave Vel = 2470
Std Dev = 18
ES = 48
High = 2491
Low = 2443
N = 5
140 gr Hornday Spire Point 43.0 grs AA4350
R-P new brass CCI-200 OAL 2.990"
2 Feb 2008 T = 52 °F
Ave Vel = 2512
Std Dev = 27
ES = 72
High = 2547
Low = 2475
N = 5
M70 Featherweight 22" Barrel
140 gr Hornady Spire Point 43.0 grs AA4350
R-P new brass CCI-200 OAL 2.990"
18 Nov 2007 T = 75 °F
Ave Vel = 2428
Std Dev = 29
ES = 95
High = 2480
Low = 2385
N = 24
easy bolt life,nice rounded primers
* Does anyone remember vacuum tubes and vacuum tube technology? I feel this analogy is totally lost on the younger generations. Might as well use the analogy of "getting a Buick for the price of a Chevy?". When all people know is Corollas and Accords, I don't know if it gets the message across.