A new update. It gets better. Or at least more amusing/amazing, depending on your viewpoint.
Our solicitor called the bank, and after a short discussion it was agreed that we would provide a letter acknowledging that the bank was demanding immediate repayment, and requesting the calculation of principal plus accrued interest up to our chosen repayment date, with no early repayment fees.
So we sent the signed letter by email (scanned pdf). They replied by email with the full amount payable.
Just to be sure, we checked the calculation. Lo and behold, they were asking for more than 3 times the accrued interest that was actually due, according to our calculation (and let's face it, this is not rocket science). This is only the accrued interest since the last installment payment date, so it is not very much (a few thousand dollars), but it just goes to show what this bank is like. So we replied by email yesterday giving our own calculation and asking them to justify theirs. They replied today, by email, saying "The outstanding is $xxxxxxxx while accrued interest is is $yyyyyy and the total repayable amount should be $zzzzzzz. Please ignore my previous email". Their new figures are almost exactly the same as ours (to within a few dollars). No apology or comment about why their original accrued interest calculation was three times the correct figure.
They also insist on having a physical copy (not scanned pdf) of our letter before proceeding. I feel like demanding that they provide the principal + interest calculation in some official document, though I don't want to pay a single cent more in interest, and I guess if we do that then it will take at least another day, so I think we will just go ahead and make the payment today.
A truly amazing bank.