@Quiltangelady ... Lots of ideas from others. And lots of ways you can work on this quilt. I hope that you ENJOY the process and the quilt owner appreciates what you are about to do for them.
I'm going to offer some thoughts from a different perspective. You have been asked to work on a treasured heirloom. Now, that may seem a bit assumptive of me, but your being asked to work on a 50yo quilt, absolutely infers such.
Be sure to discuss what can/cannot be done to the quilt, with the owner before you begin.
Point out the pros/cons/risks/options, of what you are suggesting to do.
Remember, your hesitancies towards a method ... may be totally acceptable to them.
And may be exactly what they want.
No, you don't need the person with you side-by-side for every step.
Just be sure that it is all discussed up front, before they leave, and you move ahead.
Let them decide ... and in doing so, once again, you can remind/clarify any potential downfalls of the method that they choose for you to do. And if you have concerns after you start, be sure to talk with them again.
I'm telling you this from experience ... I have been helping a friend with some of her family quilts and other textile heirlooms. She is not a quilter, but has firm ideas. Not way out ideas, but knows what she wants; and knows what is not acceptable to her. For her, she tends to want to keep things as close to the original as possible, even if it leaves an imperfect area. She can be quite OK with that imperfect area, knowing that it's had a 100 yrs (or whatever!) of wear and tear, whereas many others would not be.
As we consider options, I'm always asking her, "are you willing to accept ... ?". Or saying, "if we do this, then this ..... may happen." I am always clarifying the meaning of her thoughts/ideas, rather than being assumptive. Not being a quilter, she may use the wrong technical term ... and sometimes, if I took it literally, OMG, what a different end result we would have!!
Before you cut ... be sure to ask!! It may be obvious to you to cut it, but for the owner, it may be too upsetting to their sentimentality! Examples in your case, re the potential cutting off the binding edge, rounding the corners, etc. For my friend, she was OK with cutting off the quilt edge with the binding. But I already know that if rounded corners were suggested, it would be a no-way-jose moment ... as that is taking the quilt away from how it had been made originally by her GGM! The quilt had been totally hand-stitched, including both stages of the binding process. We had the discussion, and she was OK with machine stitching to attach, but hand stitching for the finish, and she wanted to do the hand-stitching , as a tie to her GGM.
Now that was a challenge!! ... as she is left-handed and had never sewn binding on. We started with a large mug rug, for each of us, so she could see how I did it, and reverse to left-handedness! The straight edge wasn't so bad, but corners, translated to left hand?
We had a few good laughs as we worked on our mug rugs. She left with a corner pinned, so that she could see how to do it, when she worked on her real quilt! I was SO proud of her, at how fast she worked her way around the quilt ... and how good of a job she did.
Moral of the story ... we're still friends!!
So I guess, it worked for us!
@Quiltangelady ... Good Luck to you and your friend as you go through this process.
For sure, ENJOY the process ... and I hope both of you are more than happy with the end results.