Are you casting balls, or buying 000 lead shot to shoot? I don't think you are using too small a diameter ball. YOU can play around a bit( that means to do some experimentation) with different thicknesses of patching, and different lubes, to find out what works best in your gun.
For the very best accuracy, most target shooters will use the larger, bore diameter lead balls, and a thin patch, usually lubed with Teflon, and a stout blow with their short starter to seat the ball. The ball elongates ever so little, but that improves its flight characteristics, and therefore its accuracy.
For general shooting, and hunting squirrels or small game out to 35 yards, the smaller- .350 diameter ball and a thicker patch works just fine. Try .010"- .015" patching with your .354" ball. If you find some .005" patches, try them, too. 20-40 grains of FFFg powder is pretty much the range of powder charges used in those wonderful small caliber guns, so you don't normally have to worry about Gas tearing the patches. If you find torn patches, its almost always due to some roughness in the barrel, and not the powder charge, or the thickness of the patch.
Personally, I think a .010' or .012" thick patch will work better for you with that ball than the thicker patch you are using. But, my opinion is based on my own experience, with a GM barrel, and after observing and talking to many other shooters who come out to the club range with the light caliber rifles, to kick butt at the club shoots. The only threat they normally face is from the one or two guys who shoot .32 caliber rifles!
I like to be able to start the PRB into the muzzle with thumb pressure. I have used a short starter for years, and find it annoying when a pre-cut patch catches and rolls the ball as I give the short starter a sharp whack, giving me an off-center patch and ball. When I can seat the ball with my thumb, I can " feel " the ball center in the patch properly.
This may require some work on the barrel's crown, but the end result gives me greater confidence. Done correctly, rounding the crown or even coning the bore does not diminish accuracy at all.
If you are using a short starter, make sure that the face of the jag is concave to match the Shape of the ball, so it does not misshape the lead ball when you seat the ball in the muzzle.
Oh, my reason for asking about the cast ball, is that if you buy your 000 shot as a cheap source of balls, rather than cast your own, you may not get exactly pure lead. That can explain the slight increase in diameter from a true .350. Test your lead for hardness. It should be down around 5-7 BHn if its pure lead. If you cast your own, you know what kind of lead is going into the casting, and you can control the weight, and softness of the ball much better. With that, you also get consistency in diameters.
At .352", I would not spend a lot of time or money worrying about hardness. Any given mold can give you that kind of variation in diameter. But, do check your lead for purity.
I do like to use my calipers to check the diameters of a dozen or more balls from any lot of balls I buy, just to see the range in sizes. If I find a range of more than .005", I put the balls on a scale to check the variations in weight. I don't like to see a variation of more than 1% of the total weight of the ball in those small balls.
I don't throw the rejects away- instead, they are used for casual plinking sessions or short range shooting at rabbits or squirrels, or varmints. But for target work, I don't want flyers I can't explain, so I sort the balls, by weigh and by diameter.
You also need to set aside wrinkled castings, or those with large sprues. The Sprues can be filed off, or, perhaps better, put those balls in a case tumbler, without the medium, and let them bang against each other for an hour. That usually will remove the sprue and round the balls to a consistent diameter.
Wrinkles come about because the mold or lead is not hot enough when the two meet. Keep the mold hot, and keep it close to the melting pot when you go to pour the lead into the mold, particularly if you use the open top/dipper method of casting. Don't let that dipper get cold, either. Leave it in the lead in the pot while you cool and open the mold to remove a casting. The presense of wrinkles on a small ball may cause flyers, also.
This is a lot of information, but I hope it helps you find out what your problem is. :thumbsup: