Each bank branch manager sets their own rules, so the fact one branch said they “don’t do this anymore” doesn’t mean another branch will. BB has its own issues at the moment so maybe best to avoid them anyway.
You fail to mention nationality but assuming you are from one of the 93 countries that would get a visa exempt entry. Currently that’s 60 days on entry and can extend once for 30 days if so. There is no 60 day extension.
If you enter visa exempt you’ll find it virtually impossible to open a bank account these days. An agent might be able to help you but DIY is almost impossible.
A better option is to apply for a Non O or Non OA visa prior to coming and then you’ll find opening the bank account way easier.
If you opt for the Non O then you’ll each need one and each would need their own funds in a bank account for the ongoing extensions. The advantage is you don’t need medical insurance.
If one of you gets the Non OA then the other can “piggyback” off that visa as a dependent so only one account of 800k needed. The disadvantage is the compulsory medical insurance which can be expensive depending on age.
There is no rule about how many entries you can get as a tourist. Some immigration offers may state 180 days but that rule doesn’t actually exist.
That said you’ve maxed out your time as a “tourist” and would certainly be a red flag to immigration if you tried to enter again.
No one can say if you’d have an issue but I’d bet you probably would. “A few days” isn’t likely to help. You’re not doing what a typical tourist would do and it would seem more likely you are trying to stay here long term (and therefore potentially working).
If you want to stay long term then look at the visa options that exist to do so.