Buy YNAB 4 (aka YNAB Classic). You'll have to import transactions manually, but I much prefer it to their subscription SaaS offering. I've used it for five years and love it.
You can import transactions manually into NYNAB (the new web version).
One problem I have with relying on OFX is that I have a nagging suspicion that it's not as 'official' as the statements. If there were a discrepancy between the two, I'd worry that I wouldn't be able to resolve it in my favor without having reviewed (and thus downloaded and reconciled against) the statements.
I was in your same boat until the SaaS offering started really figuring out how to do credit cards. Now, it's finally the better of the two options for me.
I use a python script to download most transactions from banks/credit cards. https://sites.google.com/site/pocketsense/home/msmoneyfixp1/...
There are enough people who do this that you can figure out how to access the OFX endpoint for most financial institutions.