A I see where my mistake is now, thanks! I suppose it makes sense that reversing the process would also meant that the 'heat intake' is equivalent to the exhaus

A I see where my mistake is now, thanks! I suppose it makes sense that reversing the process would also meant that the 'heat intake' is equivalent to the exhaust heat, which for an efficient engine wouldn't be all that much. I suppose that means that the cooling requirement will increase the energy requirement by nearly 2 orders of magnitude.