is harder better? Will this help accuracy and cut down on barrel fouling?

Typically, yes, harder is better up to a point, but there are other variables that come into play.
The 2 main causes of leading are:
1-An undersized bullet that allows expanding gas to slip by and melt off a small portion of the bullet and paste it in your barrel.
2-A bullet that is too soft for the twist rate of your barrel or a bullet that is driven too fast, thereby stripping the bullet as it moves forward.
First, you want to make sure that the finished, sized bullet is slightly larger than bore diameter. Example - with .458" bore, a bullet sized to .459-.460" typically works the best. The reasoning behind this is that you want the bullet to fill the grooves and make a tight seal. This is needed for accuracy as well to reduce / eliminate leading.
Second, gas checks can also help reduce / eliminate leading and can allow the use of a slightly softer bullet. Gas checks alone will not eliminate leading if you are going too fast.
Third, use a good bullet lube for the velocity range you are looking for.
Ultimately, you want a bullet that is hard enough to withstand your velocity goal yet not be brittle on impact. Heat treated cast bullets are very good and are available from quality companies. I use Cast Performance Bullet and Beartooth Bullets as well as casting my own un-heat treated bullets.
You did not specify which cartridge or velocity you are thinking about, but there is a big difference in bullet composition requirements between a .45acp, .44 Mag, .45-70 and a .30-06.
One of the better books is the Lyman Cast Bullet Handbook, loads of info in it.

Leading and accuracy can be caused by too hard or too soft of a bullet.

What you need to consider are the dimensions of the gun, bore, throat barrel twist and the size of the bullet. If the bullet is undersize for the guns dimensions, you'll get terrible leading from a hard bullet, while a soft bullet will often slug up and seal the bore, preventing leading, provided it isn't pushed too fast for its hardness.

I've done a fair bit of bullet casting, and find that a water quenched wheelweight bullet seems to have pretty good bullet qualities. It is hard bullet, but not really, really hard like a lyno bullet.

The mix must also have 3% TIN.