So what this comes down to is that...
1. You're absolutely certain the HDDs involved are all non-defective since in effect you've verified this.
2. There are NO OTHER PROBLEMS WITH THE SYSTEM other than the non-detection of SATA HDDs not being detected by three of the motherboard's SATA data ports/connectors that happen to be the "final" three SATA data ports on the motherboard, right?
3. You've checked (AND RECHECKED!) your BIOS settings to determine that ALL the SATA ports have been Enabled - and paid particular attention to SATA ports 3, 4, & 5? Confirm this.
4. And while it shouldn't be necessary in your case...assuming the BIOS contains SATA ports "hot-swap" or "hot-plug" settings, ensure those settings are Enabled, at least with respect to the problem SATA ports.
5. And check all your BIOS settings to ensure there's no setting that might - just might - be causing this mischief.
6. I'm just leery about the MB being defective in this situation. It could happen, of course, but it's very rare unless you had suffered some power-surge type of problem or some physical problem affecting the MB.
P.S.
If it does come down to your considering a new motherboard (I don't know any way one could "upgrade" your MB to a "270 chipset"), you would obviously be considering a new PC system. There would be no simple "upgrade" in your situation that I'm aware of.
So you're really talking about a new MB, CPU, RAM, and probably a few other "goodies", yes? In effect, a new PC.
I mention this because if that's the route you eventually take, I would strongly suggest you go with a Z370 system - not the Z270 system as you indicated. (If you were already working with a Z270 system then I would NOT upgrade.)