I don't understand "...tons of databases..." Are they all FileMaker databases?This should all be in one database, with separate tables, all related. You can use external databases and relate to tables, or import the info into new tables.
Basically you want to add tables into the student database, or add the student database table/records into the accounting database.
You could have
Students primary key (serial number) linked to Ledger with a field Student foreign key
Ledger should be linked to 2 Line Items Tables (one for Income, one for Expense
So that would be Ledger pk (serial number) to Income_LineItems fk (join table)
And the Income_LineItems should have a fk linking to an Income Table.
Repeat for an Expenses_Line Items table.
It may be much simpler to look at the Invoices starter Solution and their relationship graph