I was lucky enough to have a chat with a Tui pilot the other day and he told me they're supposedly only looking for around 6 pilots. He wasn't certain if that was across all 3 categories or if that was 6 from each. Either way, it's going to be very stiff competition... He said the recruitment team were keen to actively read each application, which is likely the reason for closing it early. Rather that than have to arbitrarily narrow the selection.
He'd only just joined the airline himself so isn't involved in recruitment but he had been briefed. That said I would class this as a full spirited rumour, but it's not called PPRuNe for nothing.