That is a good twist. Really I think you would have to be fairly certain of some kind of rescue at some point. If there was simply no hope, or you deemed the likelihood of rescue to be very slim, then it would probably change the way this question is answered.
If I thought there was a solid likelihood of rescue within a few weeks, I think I would be able to eat either one. My spouse would want me to so our kids did not have to lose both parents, as I would wish of her. My best friend would also, I would think, want me to use his body for survival if it meant that only one of our families had to lose a loved one, rather than both just because the means of survival was unpalatable. That would be my wish too, if I were the one who had died. At that point it is no longer a friend or loved one, it is a carcass.
If it means the possibility that the survivors back on the mainland or whatever did not have to suffer twice the loss then I think it would have to be considered a viable option. Imo at least.