I've been doing this for years and am currently using a Powershell
script to get Square credit card transactions and deposits into Quicken
and to import foreign stock prices into my American version of Quicken.
For the last few years, quicken has only allowed single account imports
into a small number of account types. You have a number of options to
enable imports into your "bank" accounts. Specifically, you can:
Import into "all accounts" and modify your QIF to supply the specific
account name (I think of this as one of John Pollard's contributions to
Make a dummy cash account, import your QIF file into that and then Move
the transactions into the desired account.
Create a new bank account and Move transactions from your existing
account into it. You can then just import subsequent transactions
directly into this account. This sounds like an ideal solution for you
as you know you can't download from your bank.