Is there a limit to the velocity at which a cast bullet can be pushed? Would the soft lead have a hard time with 3000fps + velocities? I'm not talking about performance on game, just holding up to the pressures and speed of some of the hotter cartridges like the UltraMags or Weatherbys.

You can pust a cast bullet as fas as you want.
BUT if you push a case bullet too fast you will have poor accurey and spend lots of time cleaning.
The speed that you can scencably push a cast bullet depends on the alloy that the bullet is made of and if the bullet has a gas check or not.
In a rifle I push HARD bullets with gas checks at 2300 fps and get little leading
I have also seen a soft pistol bullet pushed at 1200 fps and it leaded the barrel so bad that the rifling was not visabile.
IMO don't try to push a cast bullet at the 3000+ fps or pressures may build quickly do to leading from the shot before

With my experience I have figured out to minimize lead fouling its best to keep hard cast lead at around 1900 fps or less and soft lead under 1000 fps idealy with soft lead 700 to 800 fps is where you want to be but even then you still get some fouling.

HDW found the same thing I did around 1900 fps with cast bullets .

I have to back these last 2 fellows.My 30 cal cast bullets are gas checked, hard lead.I found them best at 1700fps,for best grouping.