I agree with Babore partly, in that the softer alloy is fine for the speeds you are interested in, but disagree totally about tuning loads to specific lubes. (If that is what he means.)
You state that most commercial bullets are 22 BHN. - The truth is they are advertised as such, but I haven't seen any yet that were that hard, nor would they work well if they were, because they are almost all sized to nominal diameter, which if undersize for the gun they are used in, would fail due to blow by striping lube off, if they were actually at 22 bhn. - I'm going to make a rather cold statement about commercial cast bullets. Because MOST of the people who buy them are unlearned about cast bullet technology, they buy the lowest price available, this forces all commercial casters to compete. The result is, they are selling lead they buy at wholesale, at retail prices, which pretty much fixes their profit margin so low that they can't apply a high quality lube, nor do they care because they know their customers won't know the difference.
Here are my basic recommendations for cast bullets. !. Make sure your bullets are large enough to fit the gun of interest.
2. They MUST be hard enough for the pressure they are driven at, and lubrication used. Harder than mandatory is no problem if bullets are large enough to start with.
3. Use the best lube available, which is LBT bullet lube. Nothing I know of will come close to its performance. With this lube, very soft alloys can be shot at far higher velocities than with any other lube, before leading becomes a problem. Sizing diameter will be less critical so far as leading, with softer alloys if hardness is low enough to insure obturation at the pressures of interest. Velocity range will be very broad with any alloy, in that very lite to very heavy loads can be used without leading or dramatic accuracy loss. However, best accuracy will always be with properly fitted bullets.
To put this all in a thumbnail statement. -- I don't buy the gun rag story of extensive experimentation with every powder primer, bullet etc available, to get accuracy. That is only for those reloaders who choose to be ignorant. When lead bullets are properly fitted and lubed, and as a general rule, made as hard as is cheaply possible, (don't spend a fortune on alloy) any load you choose to shoot will produce excellent accuracy if the pressures are safe.