If you are not using bank recon or cash manager then you have the steps correct and that will handle the issue. I do this with some frequency for my clients so I know it works. There should not be any aging balance issues and your aging should tie to your GL receivable balances.
There is one additional field on the ARDOC side that should be fine but you might want to check it with the following query since you are comfortable with that. This field is the perclosed field which should reflect the period the paid invoice or debit memo was closed.
select * from ardoc where custid+doctype+refnbr in (select custid+adjddoctype+adjdrefnbr from aradjust where adjbatbr = 'nnnnnn') and docbal = 0 and perclosed <> '' substitute the batch number for the nnnnnn.
The number of lines it finds can be different that the number of payment documents in the payment batch because it is possible that some payments do not clear the entire balance on an invoice and some payments may actually pay off several invoices.
If the perclosed field from the above query is showing 201301 (which I do not think it will) you could execute the following query to fix that field.
update ardoc set perclosed = 201401 where custid+doctype+refnbr in (select custid+adjddoctype+adjdrefnbr from aradjust where adjbatbr = 'nnnnnn') and docbal = 0 and perclosed <> '' substitute the batch number for the nnnnnn.
As always, it is a good idea to wrap an update statement with a begin transaction and a commit transaction line and only execute the begin transaction and update lines first to see how many lines it actually updates and then, if it matches the select statement that I provided first, execute the commit transaction. If it does not match, execute a rollback transaction and find the difference between the select statement and the update statement that is causing the variance.