My home was built in 1951 and has a large quantity of aluminum BX cable still running throughout the house. The insulation (rubber and cloth) has begun to fall apart and when I am able I am replacing this wire with either modern BX or NM cable as appropriate.

Here is the million dollar question. What, in your experience, is the best method for removing existing BX cable from the wall cavity with minimal damage to the walls? As it is my nature, I want to remove the existing BX and pull new wire through the existing chases.

I know that I could just cut off the existing cable, abandon them in the walls, drill new holes and pull new wire. However, through the years there have been a number of holes drilled through most everything in the home and I want to avoid adding any additional perforations if I can avoid it - I am beginning to fear the minimal structure is already compromised.

I know that the BX cables are typically held horizontally every so often with large cable staples, but this is less common with the vertical runs I have seen while working on other projects. Even if they are present they tend to be easily removed and I am not worried about them damaging any new wires if they can be run through the same chase.

Again, that really stems from an effective means to remove the existing BX... feels like I could attach it to my truck and I might still have problems breaking the friction hold.

You have expertly described the situation with bx, greenfield and romex. It's stapled, passed through holes in studs and plates and pretty much impossible to remove without some wallboard or plaster removal. If you have a crawl or attic space, or an unfinished basement it's not too difficult to run the new wires in these areas, using vertical runs to each outlet, once you find or create a chase from the breaker panel. Sometimes, and it's just a maybe, you can remove a small section of wallboard laterally where the bx runs, as in from outlet to outlet. Then you can cut and pull it out in sections. You could run the new wiring at that time then patch the walls. But there is no secret or magic, just some work and ingenuity at your end. And I'm sure you will get several more answers. Good luck.