Which PCIE slot are you connecting your 1x3 card into?
It is my understanding that each GPU requires a minimum of 1 PCIE lane/pipeline to transmit data. That means you would have to plug the 1x3 card into a slot with at least 3 lanes/pipelines (in the real world that means a 4x, 8x, or 16x slot). The H81 Pro BTC has a single 16x slot and five 1x slots. You could only ever run the 1x3 card on the 16x slot.
If I'm wrong on this I am open to correction. I've actually been wanting to play around with the exact setup you describe.
i plug the pcie switch card to pcie x1 slot on asus m4a78 motherboard. to x16 slot on mb plugged over usb riser r9 290. next 3x 290 plugget to pcie switch.
work fine more that 1 week on dualminer.