A question and a story for any intrepid biologists and geneticists. I'm seeing in other comments that this is fundamentally a problem with how genome sequencing works today.
When I was a movie theatre projectionist, I had a similar problem. Movies have to be assembled onto platters, from a handful of reels which contain 10-20 minute lengths of film. There's about a mile of film per hour, and to assemble it quickly you have a motorized platter and a table with its own motor with dials to control the speed of one or the other. How it should work is you take a center ring - a circle with a gap to wind film through and metal spokes that sit in the platter - and you spin the film on. You put the reels one by one onto this, stopping with each one to cut the footer of one and the header of the next to splice them together with tape.
Well, that's how it's supposed to work. Sometimes, the film tightens up, when moving the film from one platter to another. The center ring spokes might not fit, or might create additional stress.
Well, I went full speed ahead anyway, and when a tiny bit of slack resulted in a sudden jerk on the platter, the center ring popped off, and about an hour of film flew over my hand and into the wall behind me. What happened next is almost impossible to describe. A circular disk of film and metal hitting a solid wall briefly became a vertical column as the tension-less film was forced to go any direction except forward, and the result then splayed itself out on the floor in front of me in a tangled mess a mile long.
Perhaps like an early sequencing machine, my first attempt at recovering this was to look at a piece of the film and determine what part of the movie it was from, and to begin throwing away the parts I thought were from trailers.
They weren't. It was the wrong movie.
I despaired, the film was a mile long and tangled into unbelievable knots. I had to cut it to untangle it. But how?
And it hit me, I knew where a handful of colored markers were, and I began randomly pulling segments of film out from the mess, placing masking tape across a frame, and making 3 lines in 3 different colors. I made dozens of these little loops, and that was how I put it together. The process: cutting, labeling, and placing the segments into new reels made my shift from that night run into the next day's matinee.
This process was painstaking, and that's where my question leads: can we label the ends when we cut up the DNA, like I did with my film? Are we stuck watching chromosomes splash against the wall and shatter into indecipherable pieces?