I would bet you should have no issue with that setup. Pretty easy to tell you are not trying to live visa free.
If you are planning to stay with a local every time, you would need to know their address, and they would need to file appropriate forms to be fully legal. Not always checked for though. Booking a hotel for your first 2 nights would get around that issue usually, as the hotel does it for you automatically.
Other than looking for/finding a place you will reside in, the only thing I can think of is if you plan to use an agent, maybe find the agent then? Might still be too far out though.
However, depending on how/where you are calling from, and what type of phone or business etc you are calling to. It can change how you dial. You may have to add a few numbers at the front. I DO remember using 001 AND 1 in front of the +1-###-#######
Was it the exact same ID used to open both? (eg, not 2 different passports, even if the name is exactly the same?) That COULD be the issue. Otherwise, after the 5 days are finished, and if you haven't has a result, chase up with your specific branch again. This is just the banks performing KYC. This has, and will keep happening with different banks globally. And definitely more scrutiny if you are not a citizen.
As for paying rent, you should be able to send a wire from your UK bank to your landlord's account. Not sure bout anything else. I would expect there to be a way, until you sort this out.
Elite/privilege visa, if you have the cash. Otherwise, you will need to get a marriage or retirement visa with the 90 day check-ins. No need to leave the country.