I would use #4 on larger birds, rabbits maybe. 7 1/2 is for smaller birds, rodents and clay targets.
4 Buckshot is larger pellets than #4 shot, as you have already figured out.
I have heard guys say they load some bird shot first up in their HD gun and follow it up with 0 or 00 buck.
For HD, I think you would be better off with a Mossy 20 or 12 gauge. I think 00 buck in 20 gives you 7 pellets and 00 in 12 gauge gives you 9 pellets where as .410 000 buck gives 3 pellets in standard shells and 4 pellets in 3 inch shells. The 20 and 12 gauge will have better stopping power simply because your delivering more mass at about the same velocity.
To be realistic, however the bad guy in your house isnt going to notice or ask which bore shotgun you have. All will do the job, but the larger bore shells will give a better chance of stopping him dead on the first pull.