RX 580 motherboard

I suggest you might like to re-think that for a number of reasons

1. People who have multi-GPU crunching setups often report a lot more difficulty with stable and reasonably problem-free operation.  That's been my experience as well (with just 2 GPUs per host).
2. Boards with 2 x16 mechanical slots are reasonably cost effective.  I've never really checked but the prices seem to skyrocket when you need more slots than that.
3. You will need to put a lot of thought into how you will keep it all cool.
4. It's not just a matter of boards having enough x16 mechanical PCIe slots (unless you are going to invest in some sort of likely poor performance 'riser' system using x1 slots) but more to do with needing expensive processors and PCIe busses that can provide/handle the distribution of PCIe 'lanes'.  GPU performance is likely to suffer (much more than it otherwise would) if you don't get that right.  You can't just take a single GPU performance and multiply it by 4.  You really need a technical expert to come up with a design where some of the GPUs don't suffer from poor performance because of insufficient PCIe bandwidth.
5. There is not much difference between an RX570 and an RX580.  These GPUs are on 'runout' at the moment.  You might find them heavily discounted by any supplier that has excess stock to clear.  I've bought a number of RX570s recently for the equivalent of less than $US140.  Other dealers still list them much higher.  The best bang for your buck may come from an RX570 - they seem to be discounted by a larger amount.  You need to search around.
6. If you do your research and if you can get the Radeon VII for the RRP (you might have to wait for prices to settle) I would guess that your best bang for buck option might come from just one of those (to start with).  You can use a very cheap board, a cheap processor, a lower rated PSU and a lower ongoing power bill.  A single Radeon VII should produce around 1.7M credits/day (based on figures already posted).  A single RX570/580 can do a little more than 0.5M.  I think you'd be lucky if 4 of those (when you consider all likely losses when stacked together in one box) actually bettered the 1.7M of a single Radeon VII.  Even if they did, they would lose on the straight economics of capital + running costs without even considering the downtime costs when things go wrong.
7. With the advent of GPU crunching for GW tasks, you might be wise to delay a purchase until you see how that settles down.  Since GW searches are likely to ramp up in the future, you'd really like to know which GPUs perform best with those tasks.  My guess is that it might take a couple of (potentially bug ridden) months before everything settles and we get smooth operations and stable performance data.  I've set up a single RX570 system to help with the testing once a Linux app is released.  I'm expecting a bit of a roller-coaster ride :-).  I'll be quite delighted if that doesn't eventuate :-).