Well, by golly, if there is trouble to be made, I hate to be left out.
First, your choice of 4831 for a light bullet in a light load is not really appropriate. Slow powders, by their nature, give greater velocity than fast ones by sustaining their burn longer, which keeps the pressure up in the barrel longer. That means, when the bullet exits, in addition to the recoil created by accelerating the bullet and the powder mass (which is also greater with a slow powder charge) you get recoil caused by the rocket effect of the gases accelerating to still higher velocity after the bullet base clears the muzzle to let them go. This is why smaller charges of faster powder that achieve the same velocity will recoil less. Venting that muzzle pressure laterally so the rocket effect is mitigated is how rifle muzzle breaks work.
Your peak pressure with that load and bullet combination is only about 35,000 PSI. In a 24" barrel, 24% of that charge is still unburned when the bullet clears the muzzle. In an 8 lb rifle/scope combination gun, the total recoil, including the rocket effect will be almost 11 ft-lbs.
The same muzzle velocity can be achieved with only slightly more pressure (about 38,000 PSI) by using 38 grains of IMR 4198. Note how many fewer grains are needed. The ballistic efficiency (the percent of energy stored in the powder that gets converted to kinetic energy in the bullet) goes up from 19% to 27%, and the recoil drops from 11 ft-lbs to just 8 ft-lbs. The only accuracy drawback is the powder will fill the case less well. That does not matter so much with a faster powder, like IMR 4198. You can tip the muzzle up slightly before each shot to get the powder over the primer, if you want to see what difference it makes, if any, in your gun?
IMR 4198 has a top notch accuracy reputation. In the .222, I used to shoot 55 grains bullets in that caliber using a Lee loader and a scoop that gave me about 18 grains of the stuff. Thats only about 75% of case capacity, and it drilled 100 yard 10 shot groups into 1/2 an inch all day long. You will be at a little under 68% full with 38 grains. If the tipping affects accuracy (get a group tipping half your shots up and half down to see how much it opens up over just doing the former), try deburring your case flashholes to improve ignition. Also try magnum primers.
For a good method of powder charge development, look at
Dan Newberry's round robin method. The round robin can also be fired when you are located the optimum seating depth. In your shoes, I would vary the powder charge first, in the general vicinity of the 38 grain load to find a group minimum, then start monkeying with seating depth to find a minimum there. Usually there are at leas two; one with the bullet ogive 20 to 30 thousandths from touching the lands in the throat, and another when the bottom of the bullet bearing surface is around one caliber (in this case, .277") into the case neck. The former is usually the absolute best point, while the latter is still very good, but has the advantage that it is usually within SAAMI COL, so it fits in magazines O.K. for hunting.