Fitting recessed lighting without damaging ceiling
It looks as though you could actually pull this off without drilling/cutting extra holes. Yes you just drill the holes. Keep them up from the bottom, or from the top about 2" so no fasteners from the floor or drywall or plaster is hit.

I have used 3/4" bits for easy holes to pull wire through and up to 1 1/2" bits for more difficult fishing, as in threading a needle from 2 ft away. If the threading kit you speak of are fiberglass rods you connect together, these are perfect for this.

If the location of the new holes are relatively accurate how they are oriented to the joists, with care and a few drill extensions you could drill so the end of the bit can be used to pull a wire back through. It will take extra patience to do so but it can be done.

You could also use to fish tapes, or your threading kit, I presume, if you had help to send one out through the blue hole and cross it with another from the other holes, or you could go at the angle in one shot. I would assume you would pull the box at the blue location.

Here is a little sketch using you drawing to show what I would do.



From the blue hole drill 4 holes in line as best as you can with the other lights. Feed 2 wires to the fist light, one is supply, the other goes to the next light, after that it should be simple using the blue location to redirect the wires you pull to finish the remainder in that area. The rest you will need to thread.