The fairest way would be to make everyone register into pre-set groups of up to 6 people before a certain date. Then each group is given a unique ballot number. Draw numbers out of a ballot until all tickets are allocated at 9am, and email successful groups with a payment link. Give them 30 minutes to complete their payment. Any who fail to make payment , then draw out another batch and give them 30 mins to make payment. Rinse and repeat for however long it takes to sell out. At least this way, every group has a fair and equal chance of securing tickets.
I guess it depends on whether we think this iteration of Paramore could do bigger shows than 2 nights at the O2 as they did last year. I think they could - maybe not the biggest stadiums big but feels like they'd have the clout for Finsbury Park.