Thank you for your post.
I haven't worked directly with Quickbooks, but given what you have described, FileMaker Pro should be able to do this. However, don't expect this to happen overnight! You will need some time to set it up to your liking.
Yes, you can keep track of "classes", and there are several different types of reporting (columnar included with sub-summaries), and you can definitely debit or credit certain accounts directly.
If you have specific examples of what you are trying to accomplish, let me know, and I'll help guide you.
One thing to remember about most any application. If you cannot do something there was probably a REALLY good reason for you not to be able to do that.
In most accounting applications you would not key an entry directly to AR or AP control accounts because all activity should be through activity posted to a customer or a vendor (i.e. sales orders or invoices). Doing so will through you system out of balance.