I sympathise but did you make it clear from the start that you have a debt with your present supplier which SP would have to pay off for you? I would not expect any supplier to pay off debts to a third party. Normally you get a closing statement from the old supplier which has to be paid by you when you leave. 

I have not used the prepayment system butmaybe it takes overnight before the credit reaches your property? Credit updates also seem not to work at weekends and bank holidays, like bank transfers.

I think you and SP are not on the same page. Yes you can switch supplier if you are in debt to old supplier under £500 for both gas and elec,  and on a repayment meter.  And if new supplier say's it will take you on. this is called Debt Assignment Protocol. If in debt less than 28 days you can switch it will be added to final bill. If more than this you cannot switch untill you have paid the debt off. If the debt is the suppliers fault ie  estimated it wrong it will be added to final bill and you can still switch. I dont know if you are on a prepayment meter if so  then you can ask new supplier to take on your debt with your supply. I  think this is where the confusion comes in with you and SP.

If you are not on a repayment meter you can still switch,if less than 28 days but your debt will be added to final bill off your old supplier., After this you have to pay bill before you can switch. If it is the old supplier's fault you are in debt, ie incorrect  bill  they cannot stop you. You then ask new supplier to take on your debt and supply.