Using the File > Maintenance > Corrections process will not delete VAT-reconciled transactions, but it will allow you to "Reverse" them. This will add an equal and opposite transaction which will be picked up at the next VAT processing stage. You can then add the correct transactions.

You can use the Nominal Ledger > Journals system to post directly to the Nominal Ledger accounts, so yes, you can do an internal transfer - whether you can do it to control accounts I can't tell you.

But in any case, entering journal transactions requires you to understand bookkeeping principles, which I see you do, but some other Sage users reading this might not.

Also, journal entries don't have VAT calculated, so you need to work out whether and how the VAT has to be corrected.

IMHO, though, doing the customer refund then supplier refund method has one disadvantage - it shows in the audit trail, and perhaps any automatically-generated reports sent to the customer, that the customer paid some money and then got a refund, which is not actually the case.

Using the corrections method to reverse the incorrect transaction at least then shows it as a correction in the audit trail. Don't know how it would appear on reports for the customer - would it just miss the reversed transaction out or show it as having been corrected?

Yes, it shows in the audit trail - both my approach and the reversal approach do (if Sage will do that in this case*), so there's no advantage or disadvantage.

As for showing on reports sent to the customer, that's another kettle of swimmy things.

Note that the OP didn't actually say that the supplier was also a customer, only that the transaction had been posted to the customer ledger - for which the client may have created a customer account for the supplier, in which case this is isn't an issue. If the supplier is a customer as well, then obviously it depends what reports are sent out.

* A [very] quick test by loading its practice data (set to cash basis for VAT) and posting a receipt to a sales ledger account, and then reconciling a VAT return before visiting it in corrections, suggests not. It only offered me the options to delete or amend the transaction - and when hitting delete it simply refused because it was VAT reconciled.

I suspect I know why. I've long suspected the programming teams at Sage working on different parts of the software are not always in sync with one another, which I think is why there is so much inconsistency in the software's UI - and I suspect it's a similar problem here.

A reversal, as you say, is an equal and opposite transaction - so a receipt on the sales ledger would be reversed by posting a payment on the sales ledger, which is exactly what a refund is. The only difference, if Sage had given me the option, would be in the details posted for that transaction. My guess is that the team responsible for posting corrections haven't got refunds in their armoury yet. (A similar test on a VAT reconciled invoice posted a credit as a reversal, as you'd expect).