Just set up the contracts so you don’t pay them their money, or at least all their money, until you receive the VAT back from HMRC. Your worry seems to forget that the VAT they charge is only a temporary cost to you, so you just need to fund a temporary cash flow deficit or make sure that the outflow is after the inflow.
So in scenario 1 after VAT is paid and claimed you receive £1,142.86 and in the second scenario you only get £1,000 so you’re better off with the 5% rate.