You should have listened to the Accountant and not paid the £4,487.67 because that has now complicated matters further.
When HMRC do not receive a return on time, they will estimate an amount due (£4,487 in your case), and penalties and interest will be based on that estimated amount until you file an actual return.
Once you file the correct return (refund of £219.71) then HMRC will cancel the estimated amount of £4,487 and also cancel any penalties and interest because penalties and interest only apply where you owe VAT to HMRC, as your first return was a refund then no VAT is owed to HMRC and so no penalties/interest due.
However, the submitting of a return and the making of a payment can sometimes take a few days for HMRC to update their records, and there can sometime be even longer delays but usually VAT account will be updated within 7 days maximum. The debt chasing letters are sent automatically and will likely have been sent before the VAT return was filed because those letters take a few days to be produced, put into envelopes and posted 2nd class, so the debt letters could have been ignored as long as the VAT return was filed....it's a timing thing, you know you've sent the return, you know it is a refund so you just have to be patient and wait for things to update....I'm not saying ignore debt letters from HMRC, but you knew you had filed the return, but I appreciate that nobody likes debt letters.
When you paid the £4,487.67 did you ensure that you used your VAT number as the "reference" when making payment via your bank/online payment? If you make a payment to HMRC and do not use your VAT number as the payment reference, HMRC will not be able to match the payment to your VAT account and so it might be your payment is unallocated/floating around in HMRC's bank account with no home to go to. if that is the case, you need to call the VAT helpline and explain that payment was made without reference, they may ask you to write in with a copy of your bank statement showing the payment being made and that will then fix the issue....but it will not be quick, could take 3-4 weeks to resolve.
On your VAT account it originally showed you owed £4,878 then when you filed your VAT return it shows a refund of £219 (which is correct, the £4k and penalties are wiped out and replaced by the £219), had your payment of £4k been allocated to your VAT account, you would now be showing as in credit by £5,097 (£4,878 + £219) in effect you will have overpaid your VAT account by £5k but the fact the VAT account is only showing as you are due £219 then this tells me that the payment of £4k you made has not been allocated to your VAT account.
If you have paid using your VAT number as reference, then HMRC may have misallocated your payment (their error), again, you need to call HMRC and explain the situation, the £4k is not lost, it just needs to be allocated properly.
Trust that all makes sense, might need the Accountant to assist you or else you have enough in this post to call HMRC and explain the situation.