ST-4700 mated with FD-4700 and RD-4700 or RD-5800 will pretty much get you 105 5800 shifting performance at a lower price tag, 10sp consumable/wheel compatibility, and should shift better than 105 5700. There's no meaningful difference in weight between 5800 and 4700 shifters/fd, just one is 10sp and the other is 11sp.

If you went with 4700 shifters/fd and 105 everything else, you'd basically have what you wanted. Not that there's anything wrong with 11 speed.