First off, I'd sue my doctor. Implanting sextuplets is unethical and should be illegal. We're women. We do have multiple births, which is more rare and special but we do not have litters of babies. That's cat territory. And have you ever watched a mama cat who has had it with her litter? She just gets up, walks away, and the kittens fall off her boobies wherever they fall and then make their way back to bed. And then mama cat hides for awhile and spends an inordinate amount of time grooming her butt.
Secondly, I'd selectively reduce.
I don't think you could AP sextuplets WELL. You can't cosleep with each baby and gaze into each other's eyes in the middle of the night - you're always feeding or diapering someone. I would guess that their entire childhoods would be something like that.
And I would have done IUI or IVF if it had come to it. I just believe fertility treatments need to be handled more ethically.
Around here, there's a family that had six babies when my DD was born. Not only were they on TV every night complaining how much money it took to raise their babies but they always went on and on about how marvelous it was to have those babies. Two of them are/were institutionalized because of their severe brain damage due to their premature birth and have never been home with her. It may be a very nice insititution but it still isn't a mama!! And I think one is already dead due to infections. Not the greatest life for anyone.
Edited to answer the OP:
After 6 years of infertility, if I were to somehow get pregnant with 6 (NEVER would have happened) I would find myself devastated, as the CHANCES of carrying as long as Jon and Kate is super unlikely. I would feel my only choice was to reduce to twins to increase the chances of live babies at the end. It would be heartbreaking and would consume my entire pregnancy, I'm sure.
If somehow I got 6 thrust on me (Jon and Kate left them to me) I'd just try to do the best I could. No point in trying to 'GUESS' how I'd handle it when I've had ONE child for the past 8 years - I have NO idea.