Please define what you mean by later model suspension? Control arms, or a modern straight axle? If control arms, or rack and pinion steering, then it will be about the same as what I described for the Anglia.
No you don't need to build a new frame for a Morris Minor. They are a C channel frame, and boxing it should make it a very solid frame. I've seen guys put low HP V8's in them without doing anything more than just boxing the firewall forward frame rails. Some add crossmembers to stiffen, and strengthen the rest of the frame, and triangulate it.
If you're building a mainly street car, I think you can easily do so with Morris factory frame, and a little added stiffening.